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Solved Problems-7

Problems-7
A circuit is made up of a 10 Ω resistance, a 1μF capacitance and a 1 H inductance all connected in series. A voltage of 100 V at varying frequencies is applied to the circuit. Find the frequency (frequencies) at which the circuit would consume only 10% of the power it consumed at resonance.
 
Solution
Here, R­ = 10 Ω, L = 1 H, and C = 1 μF, V = 100 V
 
At resonance the current in the circuit is, Description: 3443.png
 
∴ Power consumed at resonance = Description: 3453.png
 
Let f be the frequency at which the circuit would consume only 10% of the power it consumed at resonance i.e. 100 W.
 
Under this condition, the circuit current is,
 
Description: 3459.png
 
∴ Circuit impedance, Description: 3478.png
 
∴ Circuit reactance, Description: 3484.png
 
∴ Description: 3521.png
 
⇒ Description: 3531.png
 
⇒ Description: 3538.png
 
⇒ Description: 3544.png
 




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