Question

The effective resistance of a number of resistors in parallel is x$\Omega$. When one of the resistorsis burnt, the effective resistance is y$\Omega$. The resistance of the burnt resistor is.

• A. $\left(\frac{xy}{x+y}\right)\Omega$
• B. $(y-x)\Omega$
• C. $\left(\frac{x+y}{xy}\right)\Omega$
• D. $\left(\frac{xy}{y-x}\right)\Omega$

Answer 1

The correct option is D $\left(\frac{xy}{y-x}\right)\Omega$

$\frac{1}{x}=\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}....+\frac{1}{R_n}\frac{1}{y}=\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}\frac{1}{x}=\frac{1}{R_1}+\frac{1}{y};\frac{1}{x}-\frac{1}{y}=\frac{1}{R_1}{R}_1=\frac{xy}{y-x}$