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

Step-by-step explanation:

Given

Resistor A has length
`L_1`

and Resistor B has Length
`L_2`

and Resistance is given by

`R=(\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=(V^2)/(R)`

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