Question

Figure (32-E6) shows a part of a circuit. If a current of 12 mA exists in the 5 kΩ resistor, find the currents in the other three resistors. What is the potential difference between the points A and B?

Answer 1

Let the current flowing through the resistors be marked as shown in the figure.
Given: i = 12 mA
The resistors of 20 kΩ and 10 kΩ are connected in parallel. So, the potential difference across their ends will be same, i.e.
$$\begin{gathered} 20i_1=10\left(i-i_1\right) \\ \Rightarrow 30i_1=10i \\ \Rightarrow i_1=\frac{i}{3}=\frac{12}{3}=4\mathrm{mA} \end{gathered}$$
∴ The current flowing through the 20 kΩ resistor = i₁ = 4 mA
The current flowing through the 10 kΩ resistor = i - i₁ = 8 mA
From the figure,
The current flowing through the 100 kΩ resistor = i = 12 mA

The equivalent resistance between the points A and B,
$R_{\mathrm{net}}=\left(5+\frac{20\times 10}{20+10}+100\right)\mathrm{k\Omega }=111.67\mathrm{k\Omega }$
The potential difference V between the points A and B,
$$\begin{gathered} V=i{R}_{\mathrm{net}} \\ \Rightarrow V=12\times {10}^{-3}\times 111.67\times {10}^3=1340\mathrm{V} \end{gathered}$$