One heater uses 310 W of power when connected by itself to a battery. Another heater uses 180 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

55.8W

Explanation:

P = V^2/R

R = V^2/P

For series connection

Req = R1 + R2 = V^2/310 + V^2/180

R=V^2/P = V^2/310 + V^2/180

But V^2 will cancel out

P = 1 / (1/310 + 1/180)

P = 55.8W

Given:

Heater 1:

Power, P1 = 310 W

Heater 2:

Power, P2 = 180 W

Power, P = I^2 * R

Equivalent resistance in series, Req

Req = R1 + R2

Where,

R1 = resistance in heater 1

R2 = resistance in heater 2

Total Power, Pt = V^2 * Req

Since they were connected to the same battery of voltage, V. In series connection,

= P1 + P2

P1 = V^2/R1

Req = V^2/P

= V^2/310 + V^2/180

1/Pt = (1/310 + 1/180)

= 0.0087814

Pt = 113.88 W