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:
 

 

• A. \( 1:3 \)
• B. \( 3:1 \)
• C. \( 1:2 \)
• D. \( 2:1 \)

Hint:

In a parallel circuit, currents through different branches depend on both the resistance and the potential difference across them.

Answer 1

The Correct Option is D

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: \[ I_1 : I_2 = 0.4 : 0.2 = 2:1 \]