Chapter 17, Problem 1E

If a 2.5 A current is run through a circuit for 35 minutes, how many coulombs of charge moved through the circuit?

Interpretation Introduction

Interpretation:

The coulombs of charge moved through the circuit should be calculated.

Concept Introduction:

Current is defined as the rate of charge passed through the circuit. It is mathematically represented as follows:

  $I=\frac{Q}{t}$

Here, I is current, Q is charge and t is time.

The SI unit of current is Ampere denoted by symbol A.

Thus, 1 A current means 1 C of charge is passed through a wire every 1 second.

Or,

  $1\text{ A=}\frac{1\text{ C}}{1\text{ s}}$

Answer to Problem 1E

5250 C

Explanation of Solution

Given Information:

The current passed through the wire is 2.5 A and time is 35 min.

Calculation:

The current is related to charge and time as follows:

  $I=\frac{Q}{t}$

Thus, charge can be calculated from current as:

  $Q=I\times t$

Putting the values,

  $\begin{array}{c}Q=\left(2.5\text{ A}\right)\left(35\text{ min}\right)\left(\frac{60\text{ s}}{1\text{ min}}\right)\\ =5250\text{ As}\\ =5250\text{ C}\end{array}$

Conclusion

Thus, the charge moving through the circuit is 5250 C.