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?
Question
Answer:
Explanation:
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
Answer:
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