Final answer:
To calculate the capacitance of a capacitor with a 1250V voltage and an 80A current at 1000 Hz, we use the formulas for capacitive reactance and solve for C. The result is approximately 2.04μF.
Step-by-step explanation:
To find the capacitance of the capacitor that has a voltage of 1250V at 1000 Hz and a current flow of 80A, we use the formula for capacitive reactance (XC), which relates capacitance (C), frequency (f), and current (I).
The capacitive reactance is given by:
XC = ÷V÷I
Substitute the given values:
XC = 1250 V ÷ 80 A = 15.625 Ω
Capacitive reactance is also related to the frequency (f) and capacitance (C) by the following formula:
XC = 1 ÷ (2πfC)
Now we can solve for capacitance:
C = 1 ÷ (2πfXC)
C = 1 ÷ (2π * 1000 Hz * 15.625 Ω)
C = 1 ÷ (31,415 * 15.625 Ω)
C = 1 ÷ 490690.625
C ≈ 2.04 × 10-6 F or 2.04 μF