9702/Oct Nov/13/2013/Q19

An electrical generator is started at time zero. The total electrical energy generated during the
first 5 seconds is shown in the graph.

What is the maximum electrical power generated at any instant during these first 5 seconds?

A 10 W
B 13 W
C 30 W
D 50 W

Solution:

Answer: C

Power = Energy / time

From the energy-time graph, the power generated is given by the gradient. Maximum electrical power generated at any instant is given by the gradient at that instant.

The steeper the graph, the greater the value of gradient and thus the greater the power generated. The graph is steepest between times t = 2s and t = 3s.

Consider the points: (2, 10) and (3, 40)

Maximum power = gradient = (40 – 10) / (3 – 2) = 30 W

Reference: PYQ - Oct/Nov 2013 Paper 13 Q19