The power in an electric circuit varies inversely with the resistance. If the power is 2,200watts when the resistance is 25 ohms, find the resistance when the power is 1,100watts.

50 ohms

Explanation:

From Electricity,

P ∝ 1/R

PR = k

P'R' = PR ... Equation 1

Where P' = Initial power, R' = Initial resistance, P = Final power, R = Final resistance

Make R the subject of the equation

R = P'R'/P ... Equation 2

Given: P' = 2200 watts, P = 1100 watts, R' = 25 ohms

Substitute into equation 2

R = 2200 (25) / 1100

R = 50 ohms

50ohms

Explanation:

If the power in an electric circuit varies inversely with the resistance, it can expressed as P = k/R where;

P is the power, R is the resistance and k is the constant of proportionality.

From the formula, k = PR

k = P1R1 = P2R2 ... (1)

Given P1 = 2200watts, R1 = 25ohms, P2 = 1100watts R2 = ?

From equation (1);

R2 = P1R1/P2

R2 = 2200*25/1100

R2 = 50ohms

The resistance when the power is 1100watts is 50ohms.

This shows that as the power is decreasing, the resistance is increasing.