Thursday, January 22, 2015
AC Circuits: Equivalent Reactance of a Series RLC Circuit problem #1
A 100 Ohms resistor, 5 mH inductor, and a 10 uF capacitor are connected in series to a 7V (Volts), 1kHz (kiloHertz) source. Calculate the equivalent reactance.To calculate the equivalent reactance of the circuit in the figure below, we need to use the formulas written HERE.
X_L = 2{\pi}f{L_1}
X_L = 2{\pi}(1 kHz)(5 mH)
X_L = 2{\pi}(1000 Hz)(5x10^{-3} H)
X_L = 31.42\Omega
Solving for the capacitive reactance,
X_C = \frac{1}{2{\pi}f{C_1}}
X_C = \frac{1}{2{\pi}(1kHz)(10{\mu}F)}
X_C = \frac{1}{2{\pi}(1000 Hz)(10x10^{-6}F)}
X_C = 15.92\Omega
Note: As much as possible, don't round off the values except the final answer in order to have minimal errors. This is applicable not just with this topic but to almost any.
Now, solving for the equivalent reactance,
X_{eq} = X_L - X_C
X_{eq} = 31.42\Omega - 15.92\Omega
X_{eq} = 15.5\Omega
If you have any question, place a comment below. We will solve this circuit's impedance in another post.
Update: Solution and answer for the total impedance is here!
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