Chapter 23, Problem 64A

a.

To determine

The equivalent resistance in the parallel circuit.

Answer to Problem 64A

  ${\text{R}}_t=8.89\Omega$

Explanation of Solution

Given:

Two resistors in parallel.

  ${\text{R}}_1=16\Omega$

  ${\text{R}}_2=20\Omega$

Formula Used:

Total resistance in a parallel connection is

  $\frac{1}{{\text{R}}_t}=\frac{1}{{\text{R}}_1}+\frac{1}{{\text{R}}_2}$

Calculation:

  $\frac{1}{{\text{R}}_t}=\frac{1}{{\text{R}}_1}+\frac{1}{{\text{R}}_2}$

Substituting the values.

  $\frac{1}{{\text{R}}_t}=\frac{1}{16\Omega }+\frac{1}{20\Omega }$

Simplifying

  ${\text{R}}_t=8.89\Omega$

Conclusion:

The total resistance in the parallel connection is ${\text{R}}_t=8.89\Omega$ .

b.

To determine

The total current in the circuit.

Answer to Problem 64A

The total current in the circuit is $4.5\text{A}$ .

Explanation of Solution

Given:

Potential difference ${\text{V}}_t\text{=40V}$

Total resistance ${\text{R}}_t=8.89\Omega$

Formula Used:

From Ohm’s law, total current in the circuit is

  ${\text{I}}_t=\frac{{\text{V}}_t}{{\text{R}}_t}$

Here, $V_t$ is the potential difference and $R_t$ is the equivalent resistance.

Calculations:

  ${\text{I}}_t=\frac{{\text{V}}_t}{{\text{R}}_t}$

Substitute the values

  ${\text{I}}_t=\frac{\text{40}\text{V}}{8.89\Omega }$

Simplifying

  ${\text{I}}_t=4.5\text{A}$

Conclusion:

The total current in the circuit is $4.5\text{A}$ .

c.

To determine

The current in the $16\Omega$ resistor.

Answer to Problem 64A

  $2.5\text{A}$

Explanation of Solution

Given:

Potential difference, ${\text{V}}_t\text{=40V}$

Resistance, ${\text{R}}_1=16\Omega$

Formula Used:

From Ohm’s law, total current in the circuit is

  ${\text{I}}_t=\frac{{\text{V}}_t}{{\text{R}}_t}$

Here, $V_t$ is the potential difference and $R_t$ is the equivalent resistance.

Calculations:

  ${\text{I}}_t=\frac{{\text{V}}_t}{{\text{R}}_1}$

Substituting the values

  ${\text{I}}_t=\frac{\text{40V}}{16\Omega }$

Simplifying

  ${\text{I}}_t=2.5\text{A}$

Conclusion:

The current in the $16\Omega$ resistor is $2.5\text{A}$ .