Question

Three batteries of emf $ 1 \,V $ and internal resistance $ 1 \,\Omega $ each are connected as shown. Effective emf of the combination between the points $ P $ and $ Q $ is

• A. zero
• B. $ 1\,V $
• C. $ 2 \,V $
• D. $ \frac{2}{3}V $

Answer 1

Answer: (A)

The given circuit is

Equivalent emf is given by
$\varepsilon_{eq} = \frac{2\times1}{2+1} = \frac{2}{3}$
we have,
$ \frac{E_{eq}}{\varepsilon_{eq}} = \frac{E_{1}}{\varepsilon_{1}} - \frac{E_{2}}{\varepsilon_{2}} $
$\frac{\varepsilon_{eq}}{\left(\frac{2}{3}\right)} = \frac{2}{2} - \frac{1}{1} $
$ \Rightarrow E_{eq} = 0 \,$volt