Find the rms current in a 2.0uF capacitor connected across 120V rms, 65Hz AC power.
Thanks!
To find the rms current in a capacitor connected across an AC power source, you need to use the following formula:
I = (V * 2πf * C) / √2
Where:
I is the rms current in amperes,
V is the rms voltage in volts,
f is the frequency in hertz, and
C is the capacitance in farads.
Plugging in the given values:
V = 120V
f = 65Hz
C = 2.0uF = 2.0 × 10^(-6) F
I = (120 * 2π * 65 * 2.0 × 10^(-6)) / √2
Now we can calculate the value:
I ≈ 0.0317 A (or 31.7 mA, rounded to three decimal places)
Therefore, the rms current in a 2.0uF capacitor connected across 120V rms, 65Hz AC power is approximately 31.7 mA.
To find the rms current in a capacitor connected across an AC power source, you need to use the formula:
I = V / (Xc)
Where:
I is the rms current
V is the rms voltage
Xc is the capacitive reactance
To calculate Xc, you need to use the formula:
Xc = 1 / (2πfC)
Where:
Xc is the capacitive reactance
π is approximately 3.14159
f is the frequency of the AC power source
C is the capacitance
In this case, you are given:
V = 120V rms
f = 65Hz
C = 2.0uF
First, convert the capacitance from microfarads to farads:
2.0uF = 2.0 × 10^-6 F
Next, substitute the given values into the formula to find Xc:
Xc = 1 / (2π × 65Hz × 2.0 × 10^-6 F)
Calculate the value of Xc.
Once you have Xc, substitute it and V into the first formula to find I:
I = 120V rms / Xc
Calculate the value of I to find the rms current.