In the circuit shown- cells are of equal emf E but of different internal resistances r1 - 6- and r2 - 4- - Reading of the ideal voltmeter connected across cell 1 is zero- Value of the external resistance R in ohm is equal to

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EMF and EMF Devices

In the circui...

Question

In the circuit shown, cells are of equal emf $E$ but of different internal resistances $r_{1} = 6 Ω$ and $r_{2} = 4 Ω$ . Reading of the ideal voltmeter connected across cell 1 is zero. Value of the external resistance R in ohm is equal to

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Solution

The correct option is A 2
Let, current $i$ flows through the circuit.
For current through cell 1, we can write,
$E - i r_{1} = 0$
$∴ i = \frac{E}{r_{1}}$ and for current through $R$ we can write,
$(E + E) - i (r_{1} + r_{2} + R) = 0$
$∴ i = \frac{2 E}{r_{1} + r_{2} + R}$
Using value of $i$ ,
$\frac{E}{r_{1}} = \frac{2 E}{r_{1} + r_{2} + R}$
$∴ R = r_{1} - r_{2}$
$∴ R = 6 - 4 = 2 Ω$

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In the circuit shown, cells are of equal emf E but of different internal resistances r1=6Ω and r2=4Ω . Reading of the ideal voltmeter connected across cell 1 is zero. Value of the external resistance R in ohm is equal to

The correct option is A 2Let, current i flows through the circuit.For current through cell 1, we can write,E−ir1=0∴i=Er1 and for current through R we can write,(E+E)−i(r1+r2+R)=0∴i=2Er1+r2+RUsing value of i,Er1=2Er1+r2+R∴R=r1−r2∴R=6−4=2Ω

In the circuit shown, cells are of equal emf $E$ but of different internal resistances $r_{1} = 6 Ω$ and $r_{2} = 4 Ω$ . Reading of the ideal voltmeter connected across cell 1 is zero. Value of the external resistance R in ohm is equal to