Question

When a resistance of 2 ohms is connected across the terminals of a cell, the current is 0.5 A. When the resistance is increased to 5 ohms, the current becomes 0.25 A. The e.m.f. of the cell is :-

• A. 1.0 V
• B. 1.5 V
• C. 2.0 V
• D. 2.5 V

Answer 1

The correct option is B 1.5 V

Given, $Resistance=2\Omega ,current=0.5A$ When the resistance is increased to $5\Omega$ the current is $0.25A$

The emf of the cell is$E=5\times (r+2)=\frac{1}{2}\times (r+2)....1$

When resistance is increased by $5\Omega$ the current is $0.25A$ Then, $E=0.25\times (r+5)=\left(\frac{1}{4}\right)\left(r+5\right)......2$

From equation 1 and 2 we get,

$r=1\Omega$ now put this value in equation 1 then we get $E=\frac{3}{2}=1.5v$