A circuit consists of an 92- resistor in series with a 5.9-?F capacitor, the two being...

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A circuit consists of an 92- resistor in series with a 5.9-?Fcapacitor, the two being connected between the terminals of an acgenerator. The voltage of the generator is fixed. At what frequencyis the current in the circuit one-half the value that exists whenthe frequency is very large? Note: The ac current and voltage arerms values and power is an average value unless indicatedotherwise

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3.9 Ratings (348 Votes)

Z = R + (-j)/{?*C} = R + (-j)/{2*?*f*C}
Â Â Â Â = (92)+ (-j)/{2*?*f*(5.9e-6)}
Â Â Â Â = (92)-(j)*(26989)/{f}
here ( 1/(2*pi*5.9*10^-6))=26989)
Z = {(92)² + (26989/f)²}^(1/2)Â Â

V = I*ZÂ Â Â Â ----->Â Â Â I = V/ZÂ Â Â Â ----->Â Â Â I₂/I₁ = Z₁/Z₂

When \"f\" is very large, impedance \"Z₁\" approaches{Z₁ = 120}. Thus:

I₂/I₁ = (1/2)Â Â Â Â ----->Â Â Â Z₁/Z₂ = (92)/{(92)² + (26989/f)²}^(1/2) = (1/2)

Â Â Â Â ----->Â Â Â {(92)² + (26989/f)²}^(1/2) = 184
Â Â Â Â ----->Â Â Â (92)² + (26989/f)² = 33856
Â Â Â Â ----->Â Â Â (26989/f)² = 25392
Â Â Â Â -----> 26989/f = 159.3
Â Â Â Â ----->Â Â Â Â f = 26989/159.3
Â Â Â Â ----->Â Â Â Â f = 169.4 Hz

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