Question

The battery of a car has an internal resistance of $$0.10\Omega$$ and an electromotive force of $$12V$$. When
the battery is connected to the starter motor, the potential difference across the battery terminals
is $$7.0V$$.
What is the current supplied to the starter motor?

Answer 1

Correct option is A. $$50A$$
Let the resistance of motor be $$R$$

So, current in the circuit = $$\dfrac{V}{R+r}$$

$$\implies I =\dfrac{12}{0.1+R}$$ ................(1)

Since the p.d across the motor is $$7.0\ V$$

$$\implies \dfrac{12}{0.1+R}\times R = 7.0\ V$$

$$\implies 12R = 7.0(0.1+R)$$

$$\implies R = \dfrac{0.7}{5}\Omega$$

$$\implies R = 0.14\Omega$$

So,from eq(1)

$$I = \dfrac{12}{0.1+0.14}A$$

$$\implies I = 50A$$