Q. Two batteries one of the emf $3 \, V$, internal resistance $1 \,\Omega$ and the other of emf $15 \,V$, internal resistance $2 \,\Omega$ are connected in series with a resistance $R$ as shown. If the potential difference between points $a$ and $b$ is zero, the resistance $R$ is :

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A

$5\, \Omega$

B

$7\, \Omega$

C

$3 \,\Omega$

D

$1 \,\Omega$

Solution:

We use for $3 V$ battery
$E-i r=0$
$\Rightarrow 3-\left(\frac{3+15}{1+2+R}\right)(1) =0$
Solving this equation we get,
$R=3 \,\Omega$

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