Question

An L-R-C series circuit L = 0.121 H , R = 235 Ω , and C = 7.34 μF carries an rms current of 0.455 A with a frequency of 398 Hz .

a) What average power is delivered by the source?

b) What is the average rate at which electrical energy is converted to thermal energy in the resistor?

c) What is the average rate at which electrical energy is dissipated (converted to other forms) in the capacitor?

d) What is the average rate at which electrical energy is dissipated (converted to other forms) in the inductor?

Answer 1

given

L= 0.121 H

f= 398Hz

$X_{L}=wL$

$X_{L}=2\pi fL$

$X_{L}=2\pi \times 398\times 0.121\Omega$

$X_{L}=302.59\Omega$

C=7.34*10^-6 F

$X_{C}=\frac{1}{2\pi fC}\Omega$

$X_{C}=\frac{1}{2\pi\times 398\times 7.34\times 10^{-6}}\Omega$

$X_{C}=54.480\Omega$

so the impedance

$Z=\sqrt{R^{2}+(X_{L}-X_{C})^{2}}$

$Z=\sqrt{235^{2}+(302.59-54.480)^{2}}$

$Z=341.73\Omega$

voltage

$V=IZ$

a)

power is

$P=IV$

$P=I^{2}Z$

$P=0.455^{2}\times 341.73$

$P=70.7W$

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

b)

for the resistor

V_R= IR

so the power that converted to electrical energy

$P_{R}=I^{2}R$

$P_{R}=0.455^{2}\times 398W$

$P_{R}=82.4W$

++++++++++++++++++++++++++++++

for the capacitor

$P_{C}=I^{2}X_{C}$

$P_{C}=0.455^{2}\times 54.480$

$P_{C}=11.3W$

+++++++++++++++++++++++++++++++++++++

power in inductor

$P_{L}=I^{2}L$

$P_{L}=0.455^{2}\times 302.59W$

$P_{L}=62.6W$