In an AC circuit with a frequency 25 Hz producing an rms voltage of 30 V and a 20 farad capacitor, what is the end current?
Xc = 1/2pi*F*C = 79.62 Ohms.
I = V/Xc = 30/79.62 = 0.377A = 37.7 mA.
To calculate the end current in an AC circuit with a capacitor, we need to use the formula for capacitive reactance:
Xc = 1 / (2πfC)
Where:
Xc is the capacitive reactance,
f is the frequency of the AC signal, and
C is the capacitance of the capacitor.
In this case, the frequency is 25 Hz and the capacitance is 20 F.
Let's substitute the given values into the formula:
Xc = 1 / (2π × 25 Hz × 20 F)
Now, we can solve this equation to find the value of Xc:
Xc = 1 / (1257 Hz * F)
Xc ≈ 0.000796 Ω
The capacitive reactance (Xc) is approximately 0.000796 Ω.
To find the end current (I), we use Ohm's Law:
I = V / Xc
Where:
I is the end current,
V is the voltage across the capacitor, and
Xc is the capacitive reactance.
In this case, the given voltage across the capacitor is the rms voltage of 30 V.
Substituting the values into the formula:
I = 30 V / 0.000796 Ω
Now, we can calculate the end current:
I ≈ 37688.44 A
The end current in the AC circuit is approximately 37688.44 A.