Question:
Three resistors of resistances \(10 \Omega\), \(20 \Omega\), and \(30 \Omega\) are connected as shown in the figure. If the points A, B, and C are at potentials \(10 V\), \(6 V\), and \(5 V\) respectively, then the ratio of the magnitudes of the currents through \(10 \Omega\) and \(30 \Omega\) resistors is:
Three resistors of resistances \(10 \Omega\), \(20 \Omega\), and \(30 \Omega\) are connected as shown in the figure. If the points A, B, and C are at potentials \(10 V\), \(6 V\), and \(5 V\) respectively, then the ratio of the magnitudes of the currents through \(10 \Omega\) and \(30 \Omega\) resistors is:
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In a parallel circuit, currents through different branches depend on both the resistance and the potential difference across them.
Updated On: Mar 6, 2026
- \( 1:3 \)
- \( 3:1 \)
- \( 1:2 \)
- \( 2:1 \)
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The Correct Option is D
Solution and Explanation
Using Ohm's Law \( I = \frac{V}{R} \),
For the \( 10 \Omega \) resistor:
\[
I_1 = \frac{V_A - V_B}{10} = \frac{10 - 6}{10} = \frac{4}{10} = 0.4 A
\]
For the \( 30 \Omega \) resistor:
\[
I_2 = \frac{V_B - V_C}{30} = \frac{6 - 5}{30} = \frac{1}{30} = 0.2 A
\]
Ratio:
\[
I_1 : I_2 = 0.4 : 0.2 = 2:1
\]
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