1. To calculate the effective current in the RLC circuit, we can use Ohm's Law, which states that current (I) is equal to the voltage (V) divided by the impedance (Z). Impedance in an RLC circuit is the combination of resistance (R), inductive reactance (XL), and capacitive reactance (XC).
First, we need to calculate the total impedance. The inductive reactance (XL) can be calculated using the formula XL = 2πfL, where f is the frequency (60 Hz) and L is the inductance (16.8 mH = 0.0168 H). The capacitive reactance (XC) can be calculated using the formula XC = 1/(2πfC), where C is the capacitance (0.179 μF = 0.000000179 F).
Next, we can calculate the impedance (Z) using the formula Z = √(R^2 + (XL - XC)^2).
Now we have the impedance, and we can calculate the current using the formula I = V/Z, where V is the effective voltage (139 V).
2. The power factor (PF) of the circuit is the ratio of the real power (P) to the apparent power (S). Real power represents the actual power consumed in the circuit, while apparent power is the product of the effective current and the effective voltage.
The power factor can be calculated using the formula PF = P/S. Since the power factor is the ratio of real power to apparent power, it is a dimensionless quantity.
3. The power consumed in the circuit can be calculated using the formula P = I^2 * R, where I is the effective current and R is the resistance in the circuit. This will give us the real power consumed in the circuit.
Remember to convert units appropriately throughout the calculations.
To summarize:
1. The effective current can be calculated using Ohm's Law: I = V/Z.
2. The power factor can be calculated using the formula PF = P/S.
3. The power consumed in the circuit can be calculated using the formula P = I^2 * R.
Make sure to perform the calculations and include the appropriate units in the final answers.