Question

In the figure, a current of 1 A flows through the circuit when the p.d. recorded at the ends of the parallel resistors is 1 volt. Calculate the values of R and r. 

Answer 1

E = 1.5 V; V = 1 V; I = 1 A; R = ?; r = ? 

The equivalent resistance of the parallel combination is

\[R_p = \frac{V}{I} = \frac{1}{1} = 1 \Omega\]

For resistors in parallel,

\[\frac{1}{R_p} = \frac{1}{R} + \frac{1}{3}\]

\[\Rightarrow \frac{1}{1} = \frac{1}{R} + \frac{1}{3}\]

\[\Rightarrow \frac{1}{R} = 1 - \frac{1}{3}\]

\[\Rightarrow \frac{1}{R} = \frac{2}{3}\]

\[\Rightarrow R = \frac{3}{2}\]

R = 1.5 Ω

Also, \[I = \frac{E}{R_p + r}\]

\[\Rightarrow 1 = \frac{1.5}{1 + r}\]

1 × (1 + r) = 1.5

1 + r = 1.5

r = 1.5 − 1

r = 0.5 Ω