Chapter 19, Problem 34P

To determine

The voltage across resistor $R$ in the given circuit.

Answer to Problem 34P

The voltage across resistor $R$ is $2.468\text{V}$ .

Explanation of Solution

Given information:

Consider the given circuit.

The value of the internal resistance is $0.100\Omega$ .

Formula used:

Apply Kirchhoff’s voltage law in the circuit to determine the currents.

Calculation:

Apply Kirchhoff’s voltage law in the upper loop.

  $\begin{array}{c}-2-4I_1-0.1I_2=0\\ 4I_1+0.1I_2=-2\end{array}$    … (1)

Apply Kirchhoff’s voltage law in the lower loop.

  $\begin{array}{c}-3+2+0.1I_2-0.1I_3=0\\ 0.1I_2-0.1I_3=1\end{array}$    … (2)

At node (a), apply Kirchhoff’s current law.

  $I_1=I_2+I_3$    … (3)

Substitute the value of $I_3$ from equation (3) to equation (2).

  $\begin{array}{c}0.1I_2-0.1\left(I_1-I_2\right)=1\\ -0.1I_1+0.2I_2=1\end{array}$    … (4)

On solving equations (1) and (4),

  $\begin{array}{c}{I}_1=-0.6172\text{A}\\ I_2=4.6913\text{A}\end{array}$

Substitute the values in equation (3).

  $\begin{array}{c}{I}_3=-0.6172-\left(4.6913\right)\\ =-0.5307\text{A}\end{array}$

Calculate the voltage across $4\Omega$ resistor.

  $\begin{array}{c}V=4\times \left(0.6172\right)\\ =2.468\text{V}\end{array}$

Therefore, the voltage across resistor $R$ is $2.468\text{V}$ .