Question

The following figure 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.

\[20 i_1  = 10\left( i - i_1 \right)\]

\[ \Rightarrow 30 i_1  = 10i\]

\[ \Rightarrow  i_1  = \frac{i}{3} = \frac{12}{3} = 4  mA\]

∴ 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,

\[R_{net}  = \left( 5 + \frac{20 \times 10}{20 + 10} + 100 \right)  k\Omega = 111 . 67  k\Omega\]

The potential difference V between the points A and B,

\[V = i R_{net} \]

\[ \Rightarrow V = 12 \times  {10}^{- 3}  \times 111 . 67 \times  {10}^3  = 1340  V\]