Question

A cell of e.m.f. 2 V and internal resistance 0.5 $\Omega$ is connected across a resistor R. The current that flows is same as that when a cell of e.m.f. 1.5 V and internal resistance 0.3 $\Omega$ is connected across the same resistor. Then

• A. R = 0.3 $\Omega$
• B. R = 0.6 $\Omega$
• C. R = 0.5 $\Omega$
• D. R = 0.75 $\Omega$

Answer 1

Answer: (A)

R = 0.3 $\Omega$

Answer 2

We have for the two cells:

$\frac{2}{R+0.5} = \frac{1.5}{R+0.3}$

Multiplying across:

$2(R+0.3)=1.5(R+0.5)$

Expanding both sides:

$2R + 0.6 = 1.5R + 0.75$

Rearranging:

$2R - 1.5R = 0.75 - 0.6 \Rightarrow 0.5R = 0.15$

Thus,

$R = \frac{0.15}{0.5} = 0.3\, \Omega$