Question

You have two resistors with the same cross sectional area and resistivity. Resistor A has length L1 and resistor B has length L2. Assume L2 > L1. If the resistors are connected in series with a battery, which resistor has the most power delivered to it? Explain. b: If they are connected in parallel with a battery, which resistor has the most power delivered to it? Explain.

Answer 1

Answer:

Explanation:

Given

Resistor A has length $L_1$

and Resistor B has Length $L_2$

and Resistance is given by

$R=\frac{\rho L}{A}$

Considering $\rho$and A to be constant thus

$R_2>R_1$ because $L_2>L_1$

(a)When they are connected in series

As the current in series is same and power is $i^2R$

therefore $P_2>P_1$ as R is greater for second resistor

(b)if they are connected in Parallel

In Parallel connection Voltage is same

$P=\frac{V^2}{R}$

resistance of 2 is greater than 1 thus Power delivered by 1 is greater than 2