For a resistance R and capacitance C in series, the impedance is twice that of a parallel combination of the same elements. What is the frequency of applied emf?
Text Solution
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Sol. As shown in figure, in case of series combination,
Z s = 
= [R 2 + (1/ ω C) 2 ] 1/2
In case of parallel combination,
i R = 
sin ω t and i C = 
sin 
So, I = i R + i C = 
sin ω t + 
cos ω t
i.e., i = I M sin( ω t + φ )
with I M cos φ = 
and I M sin φ = 
So, I M = 
= 
i.e. 
= 
i.e., 
and as according to given problem,
Z s = 2Z p , i.e., 
= 
i.e., 
= 4 
i.e., (1 + R 2 ω 2 C 2 ) 2 = 4R 2 ω 2 C 2
or 1 + R 2 ω 2 C 2 = 2R ω C
or (R ω C – 1) 2 = 0
or ω = 
i.e., f = 
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