Question

A toy train of mass 1 kg, starting from rest attains a velocity of $8\frac{m}{s}$ when connected to a battery of 8 volts for 4 s. Find the current in the circuit if the battery supplied a constant current during the 4-second interval. (Assume no energy loss due to friction)

• A. 1 A
• B. 2 A
• C. 3 A
• D. 4 A

Answer 1

The correct option is A

1 A

The electrical energy of the battery will be converted into mechanical energy.

Kinetic energy of the train = $\frac{1}{2}m{v}^2$ = $\frac{1}{2}\times 1\times 8^2$ = 32 J

This energy should be equal to the energy produced by battery $E$

$⟹E=qV$; $q$ is the charge supplied and $V$ is the voltage of the battery.

$qV=32J$;

$V=8volts$

$q=\frac{32}{V}$ = $\frac{32}{8}$ = 4 C

$Current\left(I\right)=\frac{charge\left(q\right)}{time\left(t\right)}$

Time $t=4s$

$⟹I=\frac{q}{t}$ = $\frac{4}{4}$ = 1A