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10 kj/s of heat is produced when a dc flows through a 100 ohm resistor. which of the followin ac produced nearly same heat per sec through the same resistor? (1)15 sinωt             (2) 45 sinωt     (3)30 sinωt              (4) 10sinωt
Asked by sumsansam | 06 Sep, 2019, 22:51: PM
answered-by-expert Expert Answer
If 10 kJ/s or 10 kW power is dissipated in 100 Ω resistor, then current is obtained as,
 
i2 × R = i2 × 100 = 10000   or  i = 10 A
 
To find the nearly same heat dissipation by ac current, we need to find rms value.
 
rms value of 15 sinωt  A:-  15/√2 = 10.6 A
rms value of 45 sinωt  A:-  45/√2 = 31.8 A
rms value of 30 sinωt  A:-  30/√2 = 21.2 A
rms value of 10 sinωt  A:-  10/√2 = 7.07 A
 
hence ac current 15 sinωt A  dissipates nearly 10 kW power in 100 Ω resistor
Answered by Thiyagarajan K | 07 Sep, 2019, 08:17: AM

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