Question

A cell supplies a current of 2A when it is connected to a $5\Omega$ resistance and supplies current of 1.2A, if it is connected to a resistance of $9\Omega$. Find the e.m.f of the cell.

• A. 6V
• B. 8V
• C. 12V
• D. 16V

Answer 1

The correct option is C

12V

Given, $I_1=2Awhen{R}_1=5\Omega$
From relation $ϵ=I(R+r)$
$ϵ=2(5+r)\dots \dots \left(i\right)$
Now, $I_2=1.2Awhen{R}_2=9\Omega$
$\therefore ϵ=1.2(9+r)\dots \dots \left(ii\right)$
From eqns. (i) and (ii)
$2(5+r)=1.2(9+r)$
or, $10+2r=10.8+1.2r$
or, $0.8r=0.8$
or, $r=\frac{0.8}{0.8}=1\Omega$
Put the value of r in eqn. (i)
$ϵ=2(5+1)=12V$
$\therefore ϵ=12V$