A circuit consisting of a capacitor and a coil in series is connected to the mains. Varying the capacitance of the capacitor, the heat power generated in the coil was increased n = 1.7 times. How much (in per cent) was the value of cos φ changed in the process?
Text Solution
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Sol. Average power
= 
In LCR circuit, Z = 
= 
For C = C 1 , 
= 
For C = C 2 , 
= 
According to problem,
= η 
∴ 
= η 
or 
+ R 2 = 
….. (1)
Power factor, cos φ = 
cos φ 1 = 
cos φ 2 = 
∴ 
+ R 2 = 
….. (2)
Similarly, 
+ R 2 = 
….. (3)
From eqns. (1), (2) and (3), we get
∴ 
+ R 2 = 
or 
= 
or cos 2 φ 2 = η cos 2 φ 1
or 
= 
∴ 
– 1 = 
– 1
∴ 
= ( 
– 1)
∴ Percentage change in cos φ is
× 100 = ( 
– 1) × 100
On putting the value we get percentage change 30%.
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