Chapter 21, Problem 42P

To determine

What is the potential difference across the coil at this moment?

Answer to Problem 42P

Solution:

The potential difference ($\Delta V$)across the coil is 7.18 V.

Explanation of Solution

Given info:

The resistor ($R$)has a value of 2.25 Ω, the current ($I$)across the inductor is $3.00A$ . The coil has an inductance ($L$) of 112 mH and the current is increasing at a rate ($\Delta I/\Delta t$ )of 3.80 A/s.

Formula used:

The potential difference ($\Delta V$) across the coil is the sum of the potential drop across the resistor and inductor and can be obtained using :

$\Delta V=IR+L\frac{\Delta I}{\Delta t}$ (1)

Where:

• $\Delta V$ is called potential difference

• $I$ is called current

• $R$ is called resistance

• $L$ is called inductance

• $\Delta I/\Delta t$ is called the rate of current

Calculation:

Inserting data given info into equation (1)we have:

$\Delta V=(3.00A)(2.25\Omega )+(0.112\text{H})(3.80A/s)$ (2)

Solving we obtain:

$\Delta V=7.18\text{ V}$ (3)

Conclusion:

According to result (3)the potential difference ($\Delta V$)across the coil is 7.18 V.