Question

A storage battery of e.m.f. $8V$ and internal resistance $0.5$$\Omega$ is being charged by a $120V$ supply using a series resistor of $15.5$$\Omega$. The terminal voltage of battery during charging is

• A. $120V$
• B. $8.5V$
• C. $11.5V$
• D. $3.5V$

Answer 1

The correct option is D

$3.5V$

Step 1: Given data:

Emf of the given battery is $E=8V$

External resistance $R=15.5$$\Omega$

Internal resistance $r=0.5$$\Omega$

Supply voltage = $120V$

Step 2: Calculating the current in the circuit,

Effective emf of the circuit

$E’=120-8=112V$

Total resistance of the given circuit

$=R+r$

$=15.5+0.5$

$=16$ $\Omega$

Current in the circuit

$$\begin{gathered} l=\frac{E}{R+r} \\ l=\frac{112}{16} \\ l=7 Ampere \end{gathered}$$

Step 3: Calculating the voltage across the terminals,

Now this is the total current in the circuit the voltage will be drop across the $R$ resistor

$V=IR$

$V=7\times 15.5$

$V=108.5volts$

The voltage across the terminals is

$=E’-V$

$=112-108.5$

$=3.5volts$

Thus, the terminal voltage across the battery is $3.5volts$.

Hence, option D is the correct answer.