A thin conducting wire carries an electric current that varies with time according to…

PHYSICS · Multi-part · GCSE · Physics · Electricity · Electricity

Problem

A thin conducting wire carries an electric current that varies with time according to a smooth curve shown verbally below. • At

t=0\,\text{s}

the current is

0.0\,\text{A}

. • The current rises steadily to

2.0\,\text{A}

t=2.0\,\text{s}

. • It then remains constant at

2.0\,\text{A}

until

t=6.0\,\text{s}

. • From

t=6.0\,\text{s}

t=8.0\,\text{s}

, it decreases linearly back to

0.0\,\text{A}

. A student claims that “the total charge that moves through the wire between

t=0\,\text{s}

and

t=8.0\,\text{s}

equals the shaded area under the current–time curve.” Respond to each part below, using clear reasoning and well-labeled mathematical expressions where appropriate. (a) Describe in words the physical meaning of the statement that the shaded area under an

I

–

t

curve equals the charge that passes through a cross-section of the wire. (b) Using the verbal description of the current variation, sketch a qualitative

I

–

t

graph on your paper. Clearly label the time and current axes with appropriate numerical values. (c) Explain, without performing detailed arithmetic, how the geometric shapes you have drawn on your graph can be used to evaluate the total charge that moves through the wire during the

8.0\,\text{s}

interval. (d) Calculate the numerical value of the total charge that passes the cross-section between

t=0\,\text{s}

and

t=8.0\,\text{s}

. Express your answer with the correct unit.

Related theory

Browse the problem library