The alternating current circuit includes 15 ohm active resistance, 30 ohm inductive resistance and 22 ohm capacitive resistance in series. What is the impedance of the circuit? Determine the voltage at the terminals of the active, inductive and capacitive resistance, if the mains voltage is 220V.
Rr = 15 ohms.
Rl = 30 ohms.
Rc = 22 ohms.
U = 220 V.
The total resistance R will be determined by the formula: R = √ (Rr ^ 2 + (Rl -Rc) ^ 2).
R = √ ((15 ohms) ^ 2 + (30 ohms – 22 ohms) ^ 2) = 17 ohms.
For a series connection of conductors, the following ratios are true:
I = Il = Ic = Ir, U = Ul = Uc = Ur.
Let’s find the current I in the circuit according to Ohm’s law: I = U / R.
I = 220 V / 17 Ohm = 12.94 A.
The voltage across the active resistance Ur = I * Rr.
Ur = 12.94 A * 15 Ohm = 194.1 V.
The voltage across the inductive reactance Ul = I * Rl.
Ul = 12.94 A * 30 Ohm = 388.2 V.
Capacitive voltage Uc = I * Rc.
Uc = 12.94 A * 22 Ohm = 284.68 V.
Answer: R = 17 ohms, Ur = 194.1 V, Ul = 388.2 V, Uc = 284.68 V.
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