Question

When a battery of emf $8V$ with internal resistance $0.5\Omega$ is charged by a $120V$ DC supply using a series resistance of $15.5\Omega$, then the terminal voltage of the battery is :

• A. $11.5V$
• B. $20V$
• C. $21.5V$
• D. $12.3V$

Answer 1

Answer: (A)

$11.5V$

Here, emf of battery $=8V$
Internal resistance of the battery, $r=0.5\Omega$
Voltage of D.C. supply $=120V$
External resistance, $R=15.5\Omega$
When the battery of emf $8V$ is charged from a DC supply of $120V$, the effective emf in the circuit is
$\epsilon =120-8=112V$
Total resistance of the circuit $=R+r$
$=(15.5+0.5)\Omega =16\Omega$
$\therefore$ Current in the circuit during charging
$I=\frac{\epsilon }{R+r}=\frac{112}{16}=7A$
$\therefore$ Terminal voltage of the battery,
$V=$ emf of the battery $+$ voltage drop across the battery
$=8+Ir=8+7\left(0.5\right)=11.5V$