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Question #165814

Two coils A and B are connected in series across a 110V, 60Hz supply. The resistance of coil A is 2  and inductance of coil B is 0.004H. If the input from the supply is 2.4kW and 1.8kVAR, find the inductance of coil A and resistance of coil B. Also calculate the voltage across each coil.

1
2021-02-25T04:10:51-0500

The frequency is 60 Hz, so, the reactance of the second coil is

"X_{2}=2\\pi fL_2=1.5\\space\\Omega."

So, since the total voltage is 110 V, the connection is series, and the active power output is 2400 W:

"P=\\frac{V^2}{R_1+R_2},\\\\\\space\\\\\nR_2=\\frac{V^2}{P}-R_1=3.04\\space\\Omega."

The voltage across the first one:

"V_1=IR_1=\\frac{V}{R_1+R_2}R_1=43.7\\text{ V},\\\\\\space\\\\\nV_2=IR_2=\\frac{V}{R_1+R_2}R_2=66.3\\text{ V}."

Find the power factor:

"\\text{ cos}\\phi=\\frac{P}{\\sqrt{P^2+Q^2}}=0.8."

The reactance of the first coil can be found from the following:

"\\text{cos}\\phi=\\frac{R_1+R_2}{\\sqrt{(R_1+R_2)^2+(X_1+X_2)^2}},\\\\\\space\\\\\nX_1=\\sqrt{\\bigg(\\frac{R_1+R_2}{\\text{cos}\\phi}\\bigg)^2-(R_1+R_2)^2}-X_2=2.28\\space\\Omega,\\\\\\space\\\\\nL_1=\\frac{X_1}{2\\pi f}=0.006\\text{ H}."

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