Chapter 23.1, Problem 1PP

To determine

The equivalent resistance of the circuit. Also, the current in the circuit.

Answer to Problem 1PP

The equivalent resistance in the circuit is $66\Omega$

The current through the circuit is $1.89\text{ A}$

Explanation of Solution

Given:

Three resistors each of 22-Ω is connected in series across a 125-V generator.

Formula used:

For a set of resistors $R_1$ , $R_2$ , $R_3$ in series, the equivalent resistance can be calculated as,

  $R_{eq}=R_1+R_2+R_3+\mathrm{...}$........(1)

For the resistance of the circuit and supply voltage, the current can be calculated using the Ohm’s law as,

  $\begin{array}{l}V=IR\\ I=\frac{V}{R}\end{array}$........(2)

Calculation:

Consider the circuit shown in Figure 1. Here, the generator is supplying a voltage of 125 V and is loaded with three resistances in series, each of resistance 22 Ω .

  

Figure 1

The equivalent resistance can be calculated using (1) as,

  $\begin{array}{c}{R}_{eq}=22+22+22\\ =66\Omega \end{array}$

Now, the current flowing through the circuit can be calculated by using the relation in (2), as

  $\begin{array}{c}I=\frac{125}{66}\\ =1.89\text{ A}\end{array}$

Conclusion:

The equivalent resistance is $66\Omega$ and the current through the circuit is1.89 A.