Asked by INimfa IMandigma on Apr 30, 2024
Verified
Three capacitors, a 12 μ F, a 20 μ F, and a 30 μ F, are connected in parallel to a 400 Hz source. What is the total XC?
A) 6.42 Ω
B) 42.78 Ω
C) 44.09 Ω
D) 56.32 Ω
Capacitive Reactance
The opposition that capacitors present to the change of voltage in AC circuits, inversely related to the frequency of the current and the capacitance.
Parallel Connection
A way of connecting electrical components in a circuit side by side, so each component is directly connected to the voltage source, and the voltage is the same across all components.
Frequency Source
A device or component that generates a steady and specific frequency of electrical signal.
- Evaluate the cumulative capacitive reactance within series and parallel capacitor circuits.
Verified Answer
ZK
Zybrea KnightMay 05, 2024
Final Answer :
A
Explanation :
The total reactance (X) of capacitors in parallel is found by the formula X=12πfCX = \frac{1}{2\pi fC}X=2πfC1 , where fff is the frequency and CCC is the total capacitance. In parallel, capacitances add up, so Ctotal=12+20+30=62μF=62×10−6FC_{total} = 12 + 20 + 30 = 62 \mu F = 62 \times 10^{-6} FCtotal=12+20+30=62μF=62×10−6F . Plugging into the formula: X=12π×400×62×10−6≈6.42ΩX = \frac{1}{2\pi \times 400 \times 62 \times 10^{-6}} \approx 6.42 \OmegaX=2π×400×62×10−61≈6.42Ω .
Learning Objectives
- Evaluate the cumulative capacitive reactance within series and parallel capacitor circuits.