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A battery of emf  $$10V$$ and internal resistance  $$3\Omega$$  is connected to a resistor. If the current in the circuit is  $$0.5A$$, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
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## QuestionPhysicsClass 12

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

$$8.5 V$$
4.6
4.6

## Solution

Here, we are given emf  $$(E)$$  as  $$10V,$$ Resistance  $$(r)$$  as  $$3\Omega$$  and current  $$I$$  is  $$0.5A.$$
$$E=10\text V$$
$$r=3\Omega$$
$$I=0.5\text A$$
Let the unknown resistance be  $$R\Omega$$ .
Using Ohm's law,
$$V=\mathit{IR}$$
$$E=I(R+r)$$
$$10=\left(0.5\right)\times (3+R)$$
$$\frac{10}{0.5}=3+R$$
$$20=R+3$$
$$R=17\Omega .$$
Hence, the resistance of the resistor will be  $$17\Omega$$ .
To verify the voltage of the battery,
$$V=\mathit{IR}$$
$$V=0.5\times 17$$
$$V=8.5\text V$$
Hence the voltage of the battery is  $$8.5\text V$$ .