Answer to Question #298020 in Electric Circuits for EDEN

Question

Calculate the power delivered to each of the resistors shown in Figure below.

An L-R-C series circuit is constructed using 175 resistor, a 12.5 capacitor, and 8.00-mH inductor, all connected across an ac source having a variable frequency and voltage amplitude of 25.0 V.

At what angular frequency will the impedance be smallest, and what is the amplitude at this frequency?

At the angular frequency in part (a), what is the maximum current through the inductor?

At the angular frequency in part (a), find the potential difference across the ac source, the resistor, the capacitor, and the inductor at the instant that the current is equal to one-half inductor it greatest positive value

In part (c), how are the potential difference across the resistor, inductor and capacitor related to the potential difference across the source.

Answer 1

1)

Angular frequency $w=\frac{1}{\sqrt{LC}}$

Put value

$$w=\frac{1}{\sqrt{8\times10^{-3}\times12.5\times10^{-6}}}=3162.27rad/sec$$

Impedance at resonance frequency

$Z_{max}=R=175\Omega$

Maximum current

$I=\frac{V}{R}=\frac{25}{175}=0.142A$

$I_L=\frac{V}{X_L}=\frac{25}{25.29}=0.98A$

Potential difference

$V_c=I\times X_L$

$V_c=0.142\times25.29=3.59V$

$$V_R=IR=0.142\times175=24.85V$$

$V_c=0.142\times25.29=3.59V$