Question:
Ten resistors, each having resistance of $6\text{ }\Omega$, are connected in a circuit. Then the ratio of maximum current to the minimum current that can flow through the circuit is:
Ten resistors, each having resistance of $6\text{ }\Omega$, are connected in a circuit. Then the ratio of maximum current to the minimum current that can flow through the circuit is:
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For $N$ identical resistors, the ratio of maximum to minimum resistance is:
$\frac{R_{\text{max}}}{R_{\text{min}}} = N^2$.
Since current is inversely proportional to resistance, the ratio of currents is also:
$\frac{I_{\text{max}}}{I_{\text{min}}} = N^2 = 10^2 = 100$.
This rule holds true regardless of the individual resistance values.
$\frac{R_{\text{max}}}{R_{\text{min}}} = N^2$.
Since current is inversely proportional to resistance, the ratio of currents is also:
$\frac{I_{\text{max}}}{I_{\text{min}}} = N^2 = 10^2 = 100$.
This rule holds true regardless of the individual resistance values.
Updated On: Jul 22, 2026
- $10:1$
- $1:10$
- $100:1$
- $1:100$
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
We need to find the ratio of the maximum current to the minimum current that can flow through a circuit consisting of ten identical $6\text{ }\Omega$ resistors connected in various configurations, assuming a constant applied voltage $V$.
Step 2: Key Formula and Approach:
By Ohm's Law, the current in a circuit under a constant voltage $V$ is:
\[ I = \frac{V}{R_{\text{eq}}} \] - The maximum current ($I_{\text{max}}$) occurs when the equivalent resistance is minimized ($R_{\text{min}}$). This is achieved when all resistors are in parallel.
- The minimum current ($I_{\text{min}}$) occurs when the equivalent resistance is maximized ($R_{\text{max}}$). This is achieved when all resistors are in series.
Step 3: Detailed Explanation:
• Calculate Minimum Resistance ($R_{\text{min}}$):
Ten resistors ($N = 10$), each of resistance $R = 6\text{ }\Omega$, are connected in parallel:
\[ R_{\text{min}} = \frac{R}{N} = \frac{6}{10} = 0.6\text{ }\Omega \]
• Calculate Maximum Resistance ($R_{\text{max}}$):
Ten identical resistors are connected in series:
\[ R_{\text{max}} = N R = 10 \times 6 = 60\text{ }\Omega \]
• Calculate the ratio of currents:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{\frac{V}{R_{\text{min}}}}{\frac{V}{R_{\text{max}}}} = \frac{R_{\text{max}}}{R_{\text{min}}} \] Substitute the resistance values:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{60}{0.6} = 100 \] The ratio of maximum current to minimum current is $100:1$.
Step 4: Final Answer:
The ratio of maximum current to minimum current is $100:1$, which corresponds to Option (C).
We need to find the ratio of the maximum current to the minimum current that can flow through a circuit consisting of ten identical $6\text{ }\Omega$ resistors connected in various configurations, assuming a constant applied voltage $V$.
Step 2: Key Formula and Approach:
By Ohm's Law, the current in a circuit under a constant voltage $V$ is:
\[ I = \frac{V}{R_{\text{eq}}} \] - The maximum current ($I_{\text{max}}$) occurs when the equivalent resistance is minimized ($R_{\text{min}}$). This is achieved when all resistors are in parallel.
- The minimum current ($I_{\text{min}}$) occurs when the equivalent resistance is maximized ($R_{\text{max}}$). This is achieved when all resistors are in series.
Step 3: Detailed Explanation:
• Calculate Minimum Resistance ($R_{\text{min}}$):
Ten resistors ($N = 10$), each of resistance $R = 6\text{ }\Omega$, are connected in parallel:
\[ R_{\text{min}} = \frac{R}{N} = \frac{6}{10} = 0.6\text{ }\Omega \]
• Calculate Maximum Resistance ($R_{\text{max}}$):
Ten identical resistors are connected in series:
\[ R_{\text{max}} = N R = 10 \times 6 = 60\text{ }\Omega \]
• Calculate the ratio of currents:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{\frac{V}{R_{\text{min}}}}{\frac{V}{R_{\text{max}}}} = \frac{R_{\text{max}}}{R_{\text{min}}} \] Substitute the resistance values:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{60}{0.6} = 100 \] The ratio of maximum current to minimum current is $100:1$.
Step 4: Final Answer:
The ratio of maximum current to minimum current is $100:1$, which corresponds to Option (C).
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