Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance a

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Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

Question Part Points Question Part Points Question Part Points Question Part Points Question Part Points A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

A 2.2 nF capacitor and a capacitor of unknown capacitance are connected in parallel across a 11 V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current has dropped to 1.2 mA. Find

(a) the unknown capacitance and
nF

(b) the lower frequency.
Hz

Question Part Points

Explanation / Answer

Here,

C1 = 2.2 nF = 2.2*10^-9 F
C2 = C
Ceq = (2.2*10^-9 + C) F

Vrms = 11 V
f = 1 kHz = 1000 Hz
I1 = 3.4 mA = 0.0034 A
I2 = 1.2 mA = 0.0012 A

as Impedance is given as :

Z = 1/2*pi*f*Ceq

V/I1 = 1/2*pi*f*Ceq ---------------------------(1)

Ceq = (0.0034 / 11) / (2*3.14*1000)

2.2*10^-9 + C = (0.0034 / 11) / (2*3.14*1000)

C = 4.70 * 10^-8 F or 4.7*10^9 nF

PART B:
Ceq = (2.2*10^-9 + C)
Ceq = (2.2*10^-9 + 4.70 * 10^-8)
Ceq = 4.92 * 10^-8 F

Eqn 1 can be written as :
V/I2 = 1 / (2*pi*f*Ceq)
(11/0.0012) = 1 / (2*3.14*f*4.92 * 10^-8)
9166.667 = 1 / (2*3.14*f*4.92 * 10^-8)
f = 1 / (2 * 3.14 * 9166.667 * 4.92 * 10^-8)

f = 353.072 Hz

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