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An LCR circuit with R=70 ohms in series with a parallel combination of L=1.5H and C=30micro faraday's is driven by a 230v supply with angular frequency of 300 rad/s (I) find the power input current ?
An LCR circuit with R=70 ohms in series with a parallel combination of L=1.5H and C=30micro faraday's is driven by a 230v supply with angular frequency of 300 rad/s (I) find the power input current ?
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ChatGPT
Sep 2
To find the power input current, we first need to calculate the impedance of the LCR circuit.
The impedance of the resistor (R) is simply R = 70 ohms.
The impedance of the inductor (L) is given by XL = ωL = 300 * 1.5 = 450 ohms.
The impedance of the capacitor (C) is given by XC = 1 / (ωC) = 1 / (300 * 30 * 10^-6) = 1 / 9 = 0.111 ohms.
Now, the total impedance of the parallel combination of L and C is given by ZLC = 1 / (1/XL + 1/XC) = 1 / (1/450 + 1/0.111) = 0.109 ohms.
The total impedance of the LCR circuit is then given by Z = sqrt(R^2 + ZLC^2) = sqrt(70^2 + 0.109^2) = 70.001 ohms.
The power input current can be calculated using Ohm's Law: I = V / Z = 230 / 70.001 = 3.285 A.
Therefore, the power input current is 3.285 A.
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Google Gemini AI
Sep 2
Step 1: Calculate the impedance of the parallel combination