Question:
Certain resistors connected in parallel and the equivalent resistance is \( X \). If one of the resistances is removed the equivalent resistance is \( Y \). What is the conductance value of removed resistance?
Certain resistors connected in parallel and the equivalent resistance is \( X \). If one of the resistances is removed the equivalent resistance is \( Y \). What is the conductance value of removed resistance?
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For parallel resistances, use \( \frac{1}{R_{\text{eq}}} \) sum rule and carefully rearrange when one resistance is removed.
Updated On: May 23, 2025
- \( \frac{XY}{Y-X} \)
- \( \frac{XY}{X-Y} \)
- \( \frac{X-Y}{XY} \)
- \( \frac{Y-X}{XY} \)
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The Correct Option is D
Solution and Explanation
For resistors in parallel:
\[
\frac{1}{X} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots
\]
When one resistor is removed:
\[
\frac{1}{Y} = \frac{1}{X} - \frac{1}{R}
\]
Rearranging:
\[
\frac{1}{R} = \frac{1}{X} - \frac{1}{Y} = \frac{Y-X}{XY}
\]
So, the conductance value of removed resistance:
\[
G = \frac{1}{R} = \frac{Y-X}{XY}
\]
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