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Question
In a series RC circuit with an AC source, R = 300 Ω, C = 25 μF, ε0 = 50 V and ν = 50/π Hz. Find the peak current and the average power dissipated in the circuit.
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Solution
Given:
Resistance of the series RC circuit, R = 300 Ω
Capacitance of the series RC circuit, C = 25 μF
Peak value of voltage, ε0 = 50 V
Frequency of the AC source, ν = 50/ `pi` Hz
Capacitive reactance (Xc) is given by,
`X_C = 1/(omegaC)`
Here, ω = angular frequency of AC source
C = capacitive reactance of capacitance
∴ `X_C = 1/(2xx50/pixx25xx10^-6)`
⇒ `X_C = 10^4/25 Ω`
Net reactance of the series RC circuit`(Z) = sqrt(R^2 + (X_C)^2`
⇒ Z =`sqrt((300)^2 + (10^4/25)^2`
= `sqrt((300)^2 + (400)^2 = 500 Ω`
(a) Peak value of current `(I_0)` is given by,
`I_0 = (epsilon_0)/z`
⇒ `I_0 = 50/500 = 0.1 A`
(b) Average power dissipated in the circuit (P) is given by,
`P = epsilon_{rms}l_{rms} cosØ`
`epsilon_{rms] = epsilon_0/sqrt2`
`∴ P = E_0/sqrt2xx I_0/sqrt2xxR/Z`
⇒ P =`(50xx0.1xx300)/(2xx500)`
⇒ `P = 3/2 = 1.5 W`
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