Question

Two identical resistors of 24 Ω each are connected to a battery of 6 V. Calculate the ratio of the power consumed by the resulting combinations with

1. Minimum resistance
2. Maximum Resistance

Answer 1

The power consumed by a resistor in an electrical circuit can be determined using the formula:

P = `V^2/R`

Where:

• P is the power consumed,
• V is the voltage across the resistor,
• R is the resistance of the resistor.

For resistors in series: total = R₁ + R₂

For resistors in parallel: `1/R_1 + 1/R_2`

Let's calculate the power consumed in this case:

a. Minimum Resistance (Parallel Configuration):

R_min = `(24 xx 24)/(24 + 24)`

= 12

I = `V/R`

= `6/12`

= 0.5 A

P = I²R

= 0.5² x 12

= 3

b. Maximum Resistance (Series Configuration):
R_max = 24 + 24 = 48

I = `V/R`

= `6/48`

= 0.125 A

P = `I^2/R`

= 0.125² × 48

= 0.75

∴ Ratio = 3 : 0.75