Answer to Question #248110 in Electrical Engineering for Kas

Question

Derive the resonant frequency for series RLC circuit. [4marks]

 for maximum power transfer. [5 marks] 

 i. The value of 𝑅𝐿

a

 ii. Find the maximum power. [5 marks] 

b

(c)Given the circuit of fig 5.1below. Determine; 

6Ω

12Ω

(b)Derive maximum power transfer formula. [4marks]

12V

 iii. State the condition for maximum power transfer. [2 marks] 

RL2A

3Ω2Ω

Answer 1

$X_L=X_C \implies 2 \pi fL=\frac{1}{2 \pi fC}\\ f^2= \frac{1}{2 \pi fL * 2 \pi fC}=\frac{1}{4 \pi^2 fLC}\\ f=\sqrt\frac{1}{4 \pi^2 fLC}\\$

i) I = I₀ (1 − e^−t/τ)   (turning on),

is the current in an RL circuit when switched on (Note the similarity to the exponential behaviour of the voltage on a charging capacitor). The initial current is zero and approaches I₀ = V/R with a characteristic time constant τ for an RL circuit, given by

$τ =\frac{ L}{ R}$

ii)

The condition for maximum power dissipation across the load is RL=RTh. That means, if the value of load resistance is equal to the value of source resistance i.e., Thevenin's resistance, then the power dissipated across the load will be of maximum value.

Power deviation

$I_L= \frac{V_{TH}}{R_{Th}+R_L}$

The power absorbed by the load is

$P_L=[\frac{V_{TH}}{R_{Th}+R_L}]^2* R_L$