Question

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

• A. 3.0
• B. 3.00
• C. 3

Answer 1

Answer: (A), (B), (C)

Let the current $I$ will flow in the anticlockwise direction.
By KVL the total voltage in the loop is equal to the net resistance of the circuit times the amount of current flowing through it,
i.e. $V_1+V_2=(r_1+r_2+R)I$

$15+3=(1+2+R)I$

or $I=\frac{18}{3+R}$

or $I=\frac{18}{3+R}$

Here, $V_{\text{ab}}=0$

or $3-1I=0$

or $I=3=\frac{18}{3+R}$

or $R=3\Omega$