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Consider a current carrying wire (current I ) in the shape of a circle. Note that as the current progresses along the wire, the direction of j (current density) changes in an exact manner, while the current I remain unaffected. The agent that is essentially responsible for is
(b) Key concept: Current per unit area (taken normal to the current), I/A, is called current density and is denoted by →J.
The SI unit of the current density are A/m2. The current density is also directed along E and which is also a vector quantity and the relationship is given by
→J=σ→E=→Eρ
where σ= conductivity and ρ= resistivity or specific resistance of the substance.
The →J changes due to the electric field produced by charges accumulated on the surface of wire.
Two batteries of emf ε1 and ε2(ε2>ε1) and internal resistances r1 and r2 respectively are connected in parallel as shown in Fig 3.1.
(a) The equivalent emf of this combination is given by
εeq =ε1r1+ε1r2(1r1+1r2)=ε1(1r1+ε2/ε1r2)(1r1+1r2)=ε2(ε1/ε2r1+1r2)(1r1+1r2)
As ε2ε1>1⇒⇒(1r1+ε2/ε1r2)(1r1+1r2)>1 or εeq>ε1 also ε1ε2<1⇒(ε1/ε2r1+1r2)(1r1+1r2)<1 or εeq<ε2
Hence ε1<εeq<ε2.
A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l1=2.9 cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?
(c) The percentage error in R can be minimised by adjusting the balance point near the middle of the bridge, i.e., when l1 is close to 50 cm . This requires a suitable choice of S.
Since,
RS=Rl1R(100−l1)=l1100−l4
Since here, R:S::2.9:97.1 imply that the S is nearly 33 times to that of R. In orded to make this ratio 1:1, it is necessary to reduce the value of S nearly 133 times i.e., nearly 3Ω.
A metal rod of length 10 cm and a rectangular cross-section of 1 cm×12 cm is connected to a battery across opposite faces. The resistance will be
(a) The resistance of wire is given by
R=ρlA
For greater value of R,l must be higher and A should be lower and it is possible only when the battery is connected across 1 cm×(12)cm (area of cross-section A ).
Which of the following characteristics of electrons determines the current in a conductor?
(a) The relationship between current and drift speed is given by
I=neAvd
Here, I is the current and vd is the drift velocity.
So, I∝vd
Thus, only drift velocity determines the current in a conductor.
Kirchhoff’s junction rule is a reflection of
(b, d)
Kirchhoff’s junction rule is also known as Kirchhoff’s current law which states that the algebraic sum of the currents flowing towards any point in an electric network is zero. i.e., charges are conserved in an electric network.
So, Kirchhoff’s junction rule is the reflection of conservation of charge.
Consider a simple circuit shown in Fig 3.2. stands for a variable resistance R′.R′ can vary from R0 to infinity. r is internal resistance of the battery (r≪R≪R0).
(a, d)
Here, the potential drop is taking place across AB and r. Since the equivalent resistance of parallel combination of R and R′ is always less than R, therefore I≥Vr+R always.
Note In parallel combination of resistances, the equivalent resistance is smaller than smallest resistance present in combination.
Temperature dependence of resistivity ρ(T) of semiconductors, insulators and metals is significantly based on the following factors:
(a, b) Resistivity is the intrinsic property of the substance.
For a metallic conductor, resistivity is given by
ρ=mne2τ
where n is the number of charge carriers per unit volume (number density) which can change with temperature T and τ is relaxation time (time interval between two successive collisions) which decreases with the increase of temperature (T∝1τ).
The measurement of an unknown resistance R is to be carried out using Wheatstones bridge (see Fig. below). Two students perform an experiment in two ways. The first students takes R2=10Ω and R1=5Ω. The other student takes R2 =1000Ω and R1=500Ω. In the standard arm, both take R3=5Ω.
Both find R=R2R1R3=10Ω within errors.
(b, c)
Given, for first student, R2=10Ω,R1=5Ω,R3=5Ω
For second student, R1=500Ω,R3=5Ω
Now, according to Wheatstone bridge rule,
R2R=R1R3⇒R=R3×R2R1…(1)
Now putting all the values in Eq. (i), we get R=10Ω for both students. Thus, we can analyse that the Wheatstone bridge is most sensitive and accurate if resistances are of same value.
Thus, the errors of measurement of the two students depend on the accuracy and sensitivity of the bridge, which inturn depends on the accuracy with which R2 and R1 can be measured.
When R2 and R1 are larger, the currents through the arms of bridge is very weak. This can make the determination of null point accurately more difficult.
In a meter bridge the point D is a neutral point (Fig 3.3).
(a, c) Key concept: Meter bridge: In case of meter bridge, the resistance wire AC is 100 cm long. Varying the position of tapping point B, bridge is balanced. If in balanced position of bridge AB=l,BC=(100−l) so that Q/P=(100−l)/l. Also P/Q=R/S=>S=100−ll×R
When there is no deflection in galvanometer there is no current across the galvanometer, then points B and D are at same potential. That point at which galvanometer shows no deflection is called null point, then potential at B and neutral point D are same. When the jockey contacts a point on the meter wire to the right of D , the potential drop across AD is more than potential drop across AB, which brings the potential of point D less than that of B, hence current flows from B to D in the galvanometer wire.
A metallic resistor is connected across a battery. If the number of collisions of the free electrons with the lattice is somehow decreased in the resistor (for example, by cooling it), the current will
(a) If the number of collisions of the free electrons with the lattice is decreased, then the drift velocity of the electrons increases.
Current i is directly proportional to the drift velocity ‘ Vd ‘ and is given by the following relation: i=neAVVd, where ‘ n ‘ is the number density of electrons and ‘ A ‘ is the area of the cross-section of the conductor.
So, we can easily see that current increases with increase in drift velocity.
Two resistors A and B have resistances RA and RB respectively with RA<RB. The resistivities of their materials are ρA and ρB.
(d) The resistance R of a conductor depends on its resistivity ρ, length l and cross-sectional area A. Thus,
R=ρlA
From the given comparison of resistances, we cannot derive the correct relation between the resistances. We also need to know the cross-sectional areas and the lengths of both the conductors before concluding about their resistivities. Only then can the relation between the resistivities be found.
The information is not sufficient to find the relation between ρA and ρB.
The product of resistivity and conductivity of a cylindrical conductor depends on
The relation between the resistivity ρ and conductivity σ of a material is given by
ρ=1σ⇒ρ×σ=1
The product of conductivity and resistivity is unity. So, this product does not depend on any of the given quantities.
As the temperature of a metallic resistor is increased, the product of its resistivity and conductivity
(c) As the temperature of a metallic resistor increases, the product of its resistivity and conductivity remains constant.
Explanation: Resistivity and conductivity are inversely proportional to each other, meaning their product is always equal to 1, regardless of temperature changes.
ρ=1σ⇒ρ×σ=1
In an electric circuit containing a battery, the charge (assumed positive) inside the battery
(b) In the study of electric current, the direction opposite the flow of electrons is regarded as the direction of flow of positive charge. In a battery, positive charge flows from the negative terminal to the positive terminal when it is discharging (connected to external circuit). But when the battery is charged, the positive charge flows from the positive terminal to the negative terminal.
A resistor of resistance R is connected to an ideal battery. If the value of R is decreased, the power dissipated in the resistor will
(a) As the resistance is connected to an ideal battery, it provides a constant potential difference across the two terminals.
The internal resistance of the battery is also zero.
The power dissipated in the resistor,
P=V2R
V is constant; hence P∝1R
Thus, if the value of the resistance is decreased, the power dissipated in the resistor will increase.
A current passes through a resistor. Let K1 and K2 represent the average kinetic energy of the conduction electrons and the metal ions respectively.
(c) Kinetic energy ( K ) is proportional to the square of velocity ( v ) according to K=12mv2, where m is mass.
Since the velocity of conduction electrons is greater than that of the metal ions, their kinetic energy is also greater.
The average kinetic energy of conduction electrons ( K1 ) is greater than that of the metal ions ( κ2 ).
Two resistors R and 2R are connected in series in an electric circuit. The thermal energy developed in R and 2R are in the ratio
The heat (thermal energy) developed in a resistor can be calculated using the formula:
H=I2RT
Where H is the heat developed, I is the current, R is the resistance, and T is the time for which the current flows.
For resistor R1 (which is R ):
H1=I2RT
For resistor R2 (which is 2R ):
H2=I2(2R)T=2I2RT
H1H2=I2RT2I2RT – Simplifying this gives: H1H2=12
Two resistances R and 2R are connected in parallel in an electric circuit. The thermal energy developed in R and 2R are in the ratio
(b) The thermal energy developed in resistor R is:
H1=V2Rt
The thermal energy developed in resistor 2R is:
H2=V22Rt
The ratio of thermal energy developed in R and 2R is:
H1H2=V2RtV22Rt
H1H2=V2Rt⋅2RV2t
H1H2=21
The ratio of thermal energy developed in R and 2R is 2:1.
A uniform wire of resistance 50Ω is cut into 5 equal parts. These parts are now connected in parallel. The equivalent resistance of the combination is
(a) Resistance of a wire is directly proportional to its length.
So, when we cut the wire into 5 equal parts, the resistance of each part will be 10Ω.
On connecting these wires in parallel, the net resistance will be
1R=110+110+110+110+110⇒R=2Ω
Consider the following two statements:
(A) Kirchhoff’s junction law follows from conservation of charge.
(B) Kirchhoff’s loop law follows from conservative nature of electric field.
(a) Kirchhoff’s junction law states that the current entering the junction is equal to the current leaving the junction, which indirectly means the charge entering the junction is equal charge leaving the junction. From the statement, it is clear that Kirchhoff’s junction law follows from the conservation of charge. Therefore, statement A is correct. Kirchhoff’s loop law states that the net potential drop in a loop is Zero ΣV= 0, which means potential changes around a closed loop is zero. Voltage is the measure of energy per unit charge in this context KVL can be restated as the total energy gained per unit charge must be equal to the amount of energy lost per unit charge (ie, Law of conservation of Energy). Therefore statement B is correct.
Two nonideal batteries are connected in series. Consider the following statements:
(A) The equivalent emf is larger than either of the two emfs.
(B) The equivalent internal resistance is smaller than either of the two internal resistances.
(b) Let the emfs of the batteries be e1 and e2, and their respective resistances be r1 and r2.
Since the batteries are connected in series, the equivalent emf will be the sum of the emf of the two batteries ( e=e1+e2 ).
Thus, e>e1 and e>e2
Thus, the equivalent emf is larger than either of the two emfs. Hence, statement A is correct.
Since the batteries are connected in series, the equivalent internal resistance (r) of the combination will be the sum of the internal resistance of the two batteries ( r=r1+r2 ).
r>r1[latex]and[latex]r>r2
Thus, the equivalent internal resistance is greater that either of the two resistances. Hence, statement B is wrong.
Two nonideal batteries are connected in parallel. Consider the following statements:
(A) The equivalent emf is smaller than either of the two emfs.
(B) The equivalent internal resistance is smaller than either of the two internal resistances.
(c) For batteries in parallel, the equivalent emf (ϵeq) can be calculated using the formula:
ϵeq=ϵ1/r1+ϵ2/r21/r1+1/r2
Thus, the equivalent emf is greater than either of the emfs. Thus, statement A is wrong.
For the parallel combination of the batteries of internal resistance r1 and r2, the equivalent internal resistance r is given as
r=r1r2r1+r2
Thus, the value of the resultant resistance is even smaller than either resistance.
The net resistance of an ammeter should be small to ensure that
(d) it does not appreciably change the current to be measured.
Explanation:
An ammeter is designed to measure the current flowing in a circuit. If the ammeter itself has a significant resistance, it will add to the overall resistance of the circuit, thereby reducing the current flowing through it. This means the measured current will not be the actual current flowing in the circuit without the ammeter. To minimize this interference and ensure an accurate measurement, the ammeter’s resistance should be as small as possible.
The net resistance of a voltmeter should be large to ensure that
(d) It does not appreciably change the potential difference to be measured.
Explanation:
A voltmeter is designed to measure voltage without significantly affecting the circuit it’s connected to. If a voltmeter had a low resistance, it would draw a substantial current from the circuit, altering the voltage being measured. By having a very high resistance, the voltmeter draws minimal current, ensuring that the measured voltage is as close as possible to the actual voltage in the circuit.
Consider a capacitor-charging circuit. Let Q1 be the charge given to the capacitor in a time interval of 10 ms and Q2 be the charge given in the next time interval of 10 ms. Let 10μC charge be deposited in a time interval t1 and the next 10μC charge is deposited in the next time interval t2.
(b) The charge Q on the plates of a capacitor at time t after connecting it in a charging circuit,
Q=ϵC(1−e−t/RC)
where
ϵ=emf of the battery connected in the charging circuit
C= capacitance of the given capacitor
R= resistance of the resistor connected in series with the capacitor
The charge developed on the plates of the capacitor in first 10 mili seconds is given by
Q1=ϵC(1−e−10×10−3/RC)
The charge developed on the plates of the capacitor in first 20 mili seconds is given by
Q′=ϵC(1−e−20×10−3/RC)
The charge developed at the plates of the capacitor in the interval t=10 mili seconds to 20 mili seconds is given by
Q2=Q′−Q1Q2=[ϵC(1−e−20×10−3/RC)]−[ϵC(1−e−10×10−3/RC)]⇒Q2=[ϵC(e−10×10−3/RC−e−20×10−3/RC)]⇒Q2=[ϵC(e−10×10−3/RC)(1−e−10×10−3/RC)]
Comparing Q1 with Q2
Q1=ϵC(1−e−10×10−3/RC),Q2=ϵCe−10×10−3/RC(1−e−10×10−3/RC)Q1Q2=1e−10×10−3/RCe−10×10−3/RC<1∴Q1>Q2
For second part of the question
10μC charge be deposited in a time interval t1 and the next 10μC charge is deposited in the next time interval t2.
The time taken for 10μC charge to develop on the plates of the capacitor is t1
10μC=ϵC(1−e−t1/RC)…(1)
The time taken for 20μC charge to develop on the plates of the capacitor is t′
20μC=ϵC(1−e−t2/RC)…(2)
Dividing (2) by (1)
20μC10μC=ϵC(1−e−t2/RC)ϵC(1−e−t1/RC)2=(1−e−t2/RC)(1−e−t1/RC)2(1−e−t1/RC)=(1−e−t2/RC)e−t2/RC=2e−t1/RC−1
Taking natural log both side,
t2RC=ln(2)+t1RC⇒t1<t2
Electrons are emitted by a hot filament and are accelerated by an electric field as shown in the figure below. The two stops at the left ensure that the electron beam has a uniform cross-section.
(a) Let the potentials at A and B be VA and VB.
As potential,
E=−dVdr
potential increases in the direction opposite to the direction of the electric field.
Thus, VA<VB
Potential energy of the electrons at points A and B :
UA=−eVA
UB=−eVB
Thus, UA>UB
Let the kinetic energy of an electron at points A and B[latex]be[latex]KA and KB respectively.
Applying the principle of conservation of mechanical energy, we get:
UA+KA=UB+KB
As, UA>UB,
KA<KB
Therefore, the speed of the electrons is more at B than at A.
A capacitor with no dielectric is connected to a battery at t=0. Consider a point A in the connecting wires and a point B in between the plates.
(b, c) As the capacitor is connected to the battery at t=0, current flows through the wire up to the time the capacitor is charged. As the capacitor is completely charged, the potential difference across the capacitor is equal to the terminal potential of the battery. So, the current stops flowing and does not pass through the point between the plates of the capacitor, as there is no medium for the flow of charge.
When no current is passed through a conductor,
(c, d) When no current passes through a conductor, free electrons do not move in a net direction. While they are constantly moving randomly due to thermal energy, there is no overall movement of electrons in a particular direction. When no current is passed through a conductor, the average of the velocities of all the free electrons at an instant is zero.
Which of the following quantities do not change when a resistor connected to a battery is heated due to the current?
(d) Resistance, resistivity and drift velocity varies with relaxation time which is dependent on temperature Number of free electrons in a conductor remain in variant even if temperature is changes.
As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity
(a) Resistivity (ρ) of a conductor is the reciprocal of the its conductivity (σ). Thus,
ρ=1σ
The ratio of the resistivity and the conductivity,
ρσ=ρ1/ρ=ρ2
As resistivity increases with temperature, the square of resistivity will also increase. Hence, the ratio of resistivity and conductivity will increase with increase in temperature.
A current passes through a wire of nonuniform cross-section. Which of the following quantities are independent of the cross section?
(a, d) Drift speed and current density are inversely proportional to the area of cross-section of a wire. Thus, they are dependent on the cross-section. The charge crossing in a given time interval is independent of the area of cross-section of the wire. Free electron density is the total number of free electrons per unit volume of the wire. The density of free electrons depends on the distribution of the free electrons throughout the volume of the wire. It does not depend on the cross-section of the wire.
Note: Drift speed is the average speed of electrons in a conductor. It is related to the current density and the cross-sectional area through the equation J=nevd (where J is current density, n is free-electron density, e is electron charge, and vd is drift speed). Since current density depends on cross-section area, drift speed also depends on it.
Mark out the correct options.
(a, d)
The ammeter is connected in series in the circuit whose current is to be measured. If the net resistance of the ammeter is high, then the amount of current that the circuit draws will have error . So, we won’t be able to accurately measure the amount of current that the circuit draws from the voltage source. Thus, it should have a small resistance.
To measure the potential difference across any circuit element, the voltmeter is connected in parallel to that circuit element. If the resistance of the voltmeter is large, then maximum voltage drop occurs across the voltmeter and it will measure the correct value of the potential.
A capacitor of capacitance 500μ F is connected to a battery through a 10kΩ resistor. The charge stored on the capacitor in the first 5 s is larger than the charge stored in the next
The charge (Q) on the capacitor at any instant t.
Q=CV(1−e−t/RC)
where
C = capacitance of the given capacitance
R= resistance of the resistor connected in series with the capacitor
RC=(10×103)×(500×10−6)=5 s
The charge on the capacitor in the first 5 seconds.
Q0=CV(1−e−5/5)=CV×0.632
The charge on the capacitor in the first 10 seconds.
Q1=CV(1−e−10/5)Q1=CV(1−e−2)=0.864×CV
Charge developed in the next 5 seconds.
Q′=Q1−Q0Q′=CV(0.864−0.632)=0.232CV
The charge on the capacitor in the first 55 seconds.
Q2=CV(1−e−55/5)Q2=CV(1−e−11)=0.99×CV
Charge developed in the next 50 seconds.
Q′=Q2−Q0Q′=CV(0.99−0.632)=0.358CV
Charge developed in the first 505 seconds.
Q3=CV(1−e−500/5)=CV(1−e−100)≈CV
Charge developed in the next 500 seconds.
Q′=CV(1−0.632)=0.368CV
Thus, the charge developed on the capacitor in the first 5 seconds is greater than the charge developed in the next 5,50,500,5000 seconds.
A capacitor C1 of capacitance 1μ F and a capacitor C2 of capacitance 2μ F are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t=0.
(b, d) Let the voltage of the battery connected to the capacitors be V. Both the capacitors will charge up to the same potential (V).
The charge on the capacitors C1[latex]is[latex]C1 V=(1μ F)×V
The charge on the capacitors C2[latex]is[latex]C2 V=(2μ F)×V
The charge on the discharging circuit at an instant t,
Q=CVe−t/RC
The current through the discharging circuit,
dQdt=−CVRCe−t/RC=VRe−t/RC
At t=0, the current through the discharging circuit will be VR for both the capacitors.
Let the time taken by the capacitor C1 to lose 50% of the charge be t1.
Q1=C1V2C1V2=C1Ve−t1/RC12=e−t1/RC
Taking natural log on both sides, we get:
−ln2=−t1RC1t1=RC1ln2
Similarly,
Time taken for capacitor C2:
t2=RC2ln2
As, C1<C2,t1<t2
Thus, we can say that C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.
The current through a wire depends on time as I=3t2+2t+5. The charge flowing through the cross-section of the wire in time interval between t=0 to t=2 s is
(a) Current,
I=dqdt=3t2+2t+5q=∫t=2t=0(3t2+2t+5)dt
Charge, q=[t3+t2+5t]20=[8+4+10]=22C
In a closed circuit, the current I (in ampere) at an instant of time t (in second) is given by I=4−0.08t. The number of electrons flowing in 50 s through the cross-section of the conductor is
Given, I=4−0.08tdqdt=4−0.08tq=∫500(4−0.08t)dtne=[4t−0.08t22]500=100n=100e=1001.6×10−19=6.25×1020 electrons
Drift velocity vd varies with the intensity of electric field as per the relation,
(a) Drift velocity, vd=eEτm∴vd∝E
The number density of free electron in a copper conductor is 8.5×1028 m−3. How long does an electron take to drift from one end of a wire, 3.0 m long to its other end? The area of cross-section of the wire is 2.0×10−6 m2 and it is carrying a current of 3.0 A.
(a) Drift velocity, vd=ineA=38.5×1028×1.6×10−19×2×10−6=0.11×10−3 ms−1∴ Time, t= length of the wire vd=30.11×10−3=2.73×104 s
Find the equivalent resistance between A and B.
(a) The points connected by a conducting wire are at same potential. Then, redraw the diagram by placing the points of same potential at one place and then solve for equivalent resistance.
Hence, from the new figure A and Y are at same potential; B and X are at same potential.
⇒1Req =16R+19R+112R=1336RReq =36R13=2.77R
Find the equivalent resistance between P and Q.
(d) It can be seen that, this diagram is symmetrical about PQ, so points on the perpendicular bisector of PQ, i.e. X,Y and Z are at same potential. So, in this type of diagrams, to calculate the equivalent resistance, we can remove the resistances at the same potential, i.e. the resistances between X and Y,Y and Z, are redundant and can be removed.
All resistances in the circuit are in parallel, 1Req =18R+14r+18R=R+r4RrReq =4RrR+rΩ
Find the equivalent resistance between A and B.
(a) Here, we have infinite pairs of R and 2R. Suppose, the equivalent resistance is R0 between C and D, i.e. excluding one pair near AB (since, pairs are infinite, equivalent resistance will remain same, if we include pair near AB ).
Req =R0=R+2RR02R+R0(R0−R)(2R+R0)=2RR02RR0−2R2+R20−RR0=2RR0R20−RR0−2R2=0R0=R±√R2+8R22=R±3R2=2R or −R
Equivalent resistance between A and B=2R(∵ equivalent resistance cannot be negative).
If e,τ and m respectively, represent the electron density, relaxation time and mass of the electron, then the resistance R of a wire of length l and area of cross-section A will be
(a) Resistance, R=ρlA and resistivity, ρ=mne2τ∴R=mlne2τA
Four wires are made of the same material and are at the same temperature. Which one of them has highest electrical resistance?
(a) The resistance R of a wire is given by R=ρlA, where ρ is the resistivity of the material, l is the length, and A is the cross-sectional area.
The area of a circle is given by A=πr2=π(d2)2=πd24, where r is the radius and d is the diameter.
Since, wires are made of same material, so resistivity ρ of all wires will be same.
Therefore, R∝lA
⇒R∝lπr2R∝l(d2)2
For length =50 cm and diameter =0.5 mm
Resistance will be maximum.
The potential difference between points A and B of the following figure is
(c) Given, circuit can be redrawn as follows
Here, I1=I2=V2Req =22×(152)=215 A
So, potential across each resistance,
V′=I1R=215×5=23 V
∴[latex]Potentialdifferenceacross,[latex]AB=23+23=43 V
In the figure given below, the current passing through 6Ω resistor is
(b)
From current division rule, i1=i(R2R1+R2)
=1.2(46+4)=1.2(410)=0.48 A
Current i as shown in the circuit will be
(b) Two resistances are short circuited.
So, only third resistance will be considered and hence,
i=V/R=10/3 A
In the circuit shown, the point B is earthed. The potential at the point A is
(b) As B is connected to the earth, so potential at B is VB=0.
Now, current in the given circuit,
i=VRnet =505+7+10+3=2 A
Potential difference between A and B is
VA−VB=2×12VA−0=24VA=24 V
A current of 2 A passes through a cell of emf 1.5 V having internal resistance of 0.15Ω. The potential difference measured in volt, across both the ends of the cell will be
(d) We have, V=E – ir =1.5−2×0.15V=1.20 V
If VAB is 4 V in the given figure, then resistance X will be
(d) Potential difference between A and B is given by VA−VB=E1r2+E2r1r1+r24=5X+2×10X+10X=20Ω
Two batteries of emf 4 V and 8 V with internal resistances 1Ω and 2Ω are connected in a circuit with a resistance of 9Ω as shown in figure. The current and potential difference between the points P and Q are
(a)
E1=4 V and E2=8 V
As, E2>E1, so current flows from Q to P.
∴i=8−412=13 A
∴ Potential difference across PQ=13×9=3 V
The current flowing through 5Ω resistance is
(d) The potentials of different points are as shown in figure below
Current through 5Ω resistance = Potential difference Resistance =(4−2)5=0.4 A
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