Question

Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in parallel across a resistor R.

Obtain expressions for

(i) current flowing in the circuit,

(ii) the terminal potential difference across the equivalent cell.

Answer 1

Given condition is shown in figure.

In parallel combination:

\(\frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}= \frac{1}{2r}+ \frac{1}{3r}+ \frac{1}{6r}\) 

r_eq = r   …(ii)

Current flowing in the circuit

\(I = \frac{E_{eq}}{R+r_{eq}} = \frac{E}{R+r}\)   …(iii)

Terminal potential difference across the equivalent cells

V = E – Ir

\(\Rightarrow V = E - \left(\frac{E}{R+r}\right)r\)

\(V = \frac{ER}{R+r}\)  …(iv)