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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?
Solution
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,
\[V = i R_{net} \]
\[ \Rightarrow V = 12 \times {10}^{- 3} \times 111 . 67 \times {10}^3 = 1340 V\]
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