Chapter 18, Problem 43P

To determine

The rms and peak currents in the resistor.

Answer to Problem 43P

The peak current is $0.55A$ .

The rms current is $0.39A$ .

Explanation of Solution

Given info:

Peak Voltage, $V_{peak}=180V$

Resistance, $R=330\Omega$

Formula used:

It is known that $I_{peak}=\frac{V_{peak}}{R}$ , where, $V_{peak}$ is peak potential difference in volts, $I_{peak}$ is peak current in amperes, and $R$ is resistance.

Formula to calculate root mean square current;

  $I_{rms}=\frac{I_{peak}}{\sqrt{2}}$

Where, $I_{peak}$ is peak current in amperes, $I_{rms}$ is root mean square current in amperes.

Calculation:

First calculate the value of peak current by substituting all the given values:

  $\begin{array}{c}{I}_{peak}=\frac{180V}{330\Omega }\\ =0.54545A\\ \simeq 0.55A\end{array}$

Now, calculate the value of root mean square current by substituting all the given values:

  $I_{rms}=\frac{0.54545A}{\sqrt{2}}=0.39A$

Conclusion: The peak current is $0.55Amp$ and the rms current is $0.39A$ .