Question

Two batteries one of emf 3 V, internal resistance 1 ohm and the other of emf 15 V, internal resistance 2 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 ohms is

• A. 5
• B. 7
• C. 3
• D. 1

Answer 1

The correct option is C 3


From circuit analysis, we get
Current flow in circuit, $i=\frac{E_{net}}{R+r}$
$i=\frac{18}{R+3}$
This current moves in the circuit from point b to a.
Applying KVL,
$V_b=-\frac{18}{R+3}\left(1\right)+3+V_a$
$V_b-V_a=0=-18+3R+9$
$[\text{given}:V_b-V_a=0]$
$\Rightarrow 3R=9$
$R=3\Omega$