Question

A battery of emf $10V$ and internal resistance $3\Omega$ is connected to a resistor. The current in the circuit is $0.5A$. The terminal voltage of the battery when the circuit is closed is:

• A. $10V$
• B. $0V$
• C. $1.5V$
• D. $8.5V$

Answer 1

The correct option is D

$8.5V$

Step 1: Given Data

Emf of the battery $\epsilon =10V$

The internal resistance of the resistor $r=3\Omega$

Current through the circuit $I=0.5A$

Let $R$ be the resistance of the resistor.

Let $V$ be the terminal voltage of the circuit.

Step 2: Calculate the resistance

According to Ohm's law, we know that

$E=I\left(R+r\right)$

$\Rightarrow R+r=\frac{E}{I}$

$\Rightarrow R=\frac{E}{I}-r$

Upon substituting the values we get,

$R=\frac{10}{0.5}-3$

$$\begin{gathered} =20-3 \\ =17\Omega \end{gathered}$$

Step 3: Calculate the Terminal Voltage

According to Ohm's law, we know that

$V=IR$

Upon substituting the values we get,

$V=0.5A\times 17\Omega$

$=8.5V$

Hence, the terminal voltage of the battery when the circuit is closed is $8.5V$.

Therefore the correct answer is option (D).