Question:
The ratio of the rate of flow of electrons through three resistors connected in parallel to a voltage source $V$ is $3 : 2 : 1$, then the ratio of their respective resistance values is
The ratio of the rate of flow of electrons through three resistors connected in parallel to a voltage source $V$ is $3 : 2 : 1$, then the ratio of their respective resistance values is
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For parallel circuits:
- Same voltage across all resistors
- Current $\propto \frac{1}{R}$
Updated On: Apr 30, 2026
- $1 : 1 : 1$
- $6 : 3 : 2$
- $2 : 3 : 6$
- $9 : 4 : 1$
- $\sqrt{6} : \sqrt{4} : \sqrt{2}$
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The Correct Option is C
Solution and Explanation
Concept:
Rate of flow of electrons $\propto$ current $I$.
For parallel connection, voltage across each resistor is same: \[ I = \frac{V}{R} \Rightarrow I \propto \frac{1}{R} \]
Step 1: Given current ratio.
\[ I_1 : I_2 : I_3 = 3 : 2 : 1 \]
Step 2: Relate to resistance.
\[ R \propto \frac{1}{I} \]
Step 3: Find resistance ratio.
\[ R_1 : R_2 : R_3 = \frac{1}{3} : \frac{1}{2} : 1 \]
Step 4: Simplify ratio.
Multiply by $6$: \[ R_1 : R_2 : R_3 = 2 : 3 : 6 \]
For parallel connection, voltage across each resistor is same: \[ I = \frac{V}{R} \Rightarrow I \propto \frac{1}{R} \]
Step 1: Given current ratio.
\[ I_1 : I_2 : I_3 = 3 : 2 : 1 \]
Step 2: Relate to resistance.
\[ R \propto \frac{1}{I} \]
Step 3: Find resistance ratio.
\[ R_1 : R_2 : R_3 = \frac{1}{3} : \frac{1}{2} : 1 \]
Step 4: Simplify ratio.
Multiply by $6$: \[ R_1 : R_2 : R_3 = 2 : 3 : 6 \]
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