Chapter 23.1, Problem 10PP

To determine

Thevoltage across the third resistance of the circuit.

Answer to Problem 10PP

The voltage across the third resistance is $7.5\text{}\text{ V}$.

Explanation of Solution

Given:

Three resistors are connected in series across a 12-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)

Also, in the series circuit, same current flows through the resistors and the supply voltage can be expressed as the product of the current and the equivalent resistance using the Ohm’s Law as,

  $\begin{array}{c}V=I{R}_{eq}\\ =I\left(R_1+R_2+R_3+\mathrm{...}\right)\end{array}$ …… (2)

The above equation implies that the supply voltage is the sum of the individual potential differences across the resistors. So, the voltage across one of the resistors can be found if the potential differences across other resistors and the supply voltage are known.

Calculation:

Consider the circuit shown in Figure 1. Here, the generator is supplying a voltage of 12-V and is loaded with three resistances in series.

  

Figure 1

The unknown potential difference $V_3$ can be calculated using (2) as,

  $\begin{array}{c}V=V_1+V_2+V_3\\ V_3=V-V_1-V_2\\ =12-1.2-3.3\\ =7.5\text{ V}\end{array}$

Conclusion:

The voltage across the third resistance is 7.5 V.