Chapter 23.1, Problem 11PP

a.

To determine

Theequivalent resistance of the circuit.

Answer to Problem 11PP

The equivalent resistance in the circuit is $55\Omega$.

Explanation of Solution

Given:

Two resistors of value 22 Ω, and 33 Ω are connected in series across a 120-V battery.

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)

Calculation:

Consider the circuit shown in Figure 1. Here, the generator is supplying a voltage of 120-V and is loaded with two resistances in series , 22 Ω and 33 Ω.

  

Figure 1

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

  $\begin{array}{c}{R}_{eq}=22+33\\ =55\Omega \end{array}$

Conclusion:

The equivalent resistance of the circuit is $R_{eq}=55\Omega$ .

b.

To determine

The current in the circuit.

Answer to Problem 11PP

The current through the circuit is $\text{2}\text{.18 A}$.

Explanation of Solution

Given:

Two resistors of value 22 Ω, and 33 Ω are connected in series across a 120-V battery.

Formula used:

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:

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

  $\begin{array}{c}I=\frac{120}{55}\\ =2.18\text{ A}\end{array}$

Conclusion:

The current through the circuit is 2.18 A.

c.

To determine

Thetotal potential difference across each of the resistors.

Answer to Problem 11PP

The potential differences across each resistor are $V_{22}=48\text{ V}$ , $V_{33}=72\text{ V}$ .

Explanation of Solution

Given:

Two resistors of value 22 Ω, and 33 Ω are connected in series across a 120-V battery.

Formula used:

The potential difference across each of the resistors is the product of the current through the circuit and the resistance value given by,

  $V=IR$

Calculation:

The individual potential difference across the resistors can be calculated using (1) as follows.

  $\begin{array}{c}{V}_{22\Omega }=22\times 2.181\\ =48\text{ V}\end{array}$

  $\begin{array}{c}{V}_{33\Omega }=33\times 2.181\\ =72\text{ V}\end{array}$

(It is to be noted that since there are only two resistors,having found voltage across one resistance, the other can also be found as the difference of supply voltage and the voltage across the first resistor.)

Conclusion:

The potential difference across each of the individual resistors are $V_{22\Omega }=48\text{ V}$ and $V_{33\Omega }=72\text{ V}$ .