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Question


i=15sinωt+20cosωt.
Alternating current  i is passed through a resistance of 8Ω. Find the heat developed across R in 10 seconds.
  1. 25×103 J
  2. 125×102 J
  3. 625×102 J
  4. 5×104 J


Solution

The correct option is A 25×103 J
i=15sinωt+20cosωt
=25{1525sinωt+2025cosωt}=25{sinωtcos53+cosωtsin53}
i=25sin(ωt+53)
irms=252Heat (Q)=Power×t=i2rmsRt
Q  =i2rmsRt
=(252)28×10=6252×8×10
=2500×10=25×103J

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