Question

A resistor of power \(P_1\) at voltage \(V_1\) is connected in series with another resistor of power \(P_2\) at voltage \(V_2\). The equivalent resistance will be:

• A. \(\frac{V_1^2}{P_1} + \frac{V_2^2}{P_2}\)
• B. \(\frac{P_1^2}{V_1} + \frac{P_2^2}{V_2}\)
• C. \(\frac{P_1 + P_2}{(V_1 + V_2)^2}\)
• D. \(\frac{P_1}{V_1^2} + \frac{P_2}{V_2^2}\)

Hint:

For resistors in series, the total resistance is the sum of individual resistances.

Answer 1

The Correct Option is A

When two resistors are connected in series, the equivalent resistance \(R_{\text{eq}}\) is the sum of individual resistances. Using the formula \(R = \frac{V^2}{P}\) for each resistor, the equivalent resistance becomes: \[ R_{\text{eq}} = \frac{V_1^2}{P_1} + \frac{V_2^2}{P_2} \]