Question

When a battery connected across a resistor of 16$\Omega$ , the voltage across the resistor is 12 V. When the same battery is connected across a resistor of 10$\Omega$ , voltage across it is 11V. The internal resistance of the battery in Ohms is

• A. $10/7$
• B. $20/7$
• C. $25/7$
• D. $30/7$

Answer 1

The correct option is B $20/7$

case 1 :-
$E_R=I\times R$
$E_R=\left(\frac{E}{R+r}\right)R$

$12=\frac{16E}{16+r}$ ...........(1)
case 2:-
$E_R=IR$
$E_R=\left(\frac{E}{R+r}\right)R$

$11=\frac{10E}{10+R}$ ...............(2)
$\frac{12}{16}(16+r)=\frac{11}{10}(10+r)$
$15(16+r)=22(10+r)$
$240+15r=220+22r$
$7r=20$
$r=\frac{20}{7}\Omega$