Chapter 19, Problem 77GP

To determine

The possible values of the terminal voltage $V_{\text{ba}}$ in the given circuit.

Answer to Problem 77GP

The possible values of the terminal voltage $V_{\text{ba}}$ are $52.3\text{V}$ and $-28.3\text{V}$ .

Explanation of Solution

Given information:

Consider the given circuit.

Formula used:

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

Calculation:

Since, the current across $4\text{k}\Omega$ resistor is $3.50\text{mA}$ . Calculate the voltage across nodes c and d using Ohm’s law.

  $\begin{array}{c}{V}_{\text{cd}}=4\times {10}^3\times 3.50\times {10}^{-3}\\ =14\text{V}\end{array}$

  $4\text{k}\Omega$ resistor and $\text{8}\text{k}\Omega$ are connected in parallel. So, the voltage across the node will be same.Let $I_{\text{ef}}$ is the current through $\text{8}\text{k}\Omega$ resistor. Calculate the value of the current using Ohm’s law.

  $\begin{array}{c}{I}_{\text{ef}}=\frac{14}{8\times {10}^3}\\ =1.75\text{mA}\end{array}$

Calculate the total current flowing through $5\text{kΩ}$ resistor.

  $\begin{array}{c}I=1.75+3.50\\ =5.25\text{mA}\end{array}$

Since the value of the voltage $V_{\text{ba}}$ is not given. Calculate the value of the terminal voltage $V_{\text{ba}}$ when current flowing towards $5\text{kΩ}$ resistor using Kirchhoff’s voltage law.

  $\begin{array}{c}-V_{\text{ba}}+\left(5\text{kΩ}\right)I+14+12+1\cdot I=0\\ -V_{\text{ba}}+\left(5001\right)I+26=0\end{array}$

… (1)

Substitute the value of the current in equation (1).

  $\begin{array}{c}-V_{\text{ba}}+\left(5001\right)\left(5.25\times {10}^{-3}\right)+26=0\\ V_{\text{ba}}=52.3\text{V}\end{array}$

Calculate the value of the terminal voltage $V_{\text{ba}}$ when current flowing away from $5\text{kΩ}$ resistor using Kirchhoff’s voltage law.

  $\begin{array}{c}{V}_{\text{ba}}+\left(5\text{kΩ}\right)I+14-12+1\cdot I=0\\ V_{\text{ba}}=-\left(5001\right)I-2\\ =-\left(5001\right)\times 5.25\times {10}^{-3}-2\\ =-28.3\text{V}\end{array}$

Therefore, the possible values of the terminal voltage $V_{\text{ba}}$ are $52.3\text{V}$ and $-28.3\text{V}$ .