Math Problem Statement
Solution
This is a question about an RLC circuit where you're asked to find the current (in amperes) in the circuit. The given values are:
- Resistance (R) = 25 Ω
- Inductance (L) = 0.5/π H
- Capacitance (C) = 200/π µF
- Voltage (V) = 200 V
- Frequency (f) = 50 Hz
To find the current, we will calculate the total impedance (Z) of the circuit and then use Ohm's Law:
Where:
- is the inductive reactance
- is the capacitive reactance
Once we calculate , the current is given by:
I will now proceed with the calculations.
Let me know if you'd like me to explain any step further or clarify any detail!
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Math Problem Analysis
Mathematical Concepts
Impedance in RLC Circuits
Inductive Reactance
Capacitive Reactance
Ohm's Law
Formulas
Z = √(R^2 + (X_L - X_C)^2)
X_L = 2\pi f L
X_C = 1/(2\pi f C)
I = V / Z
Theorems
Ohm's Law
Impedance in AC Circuits
Suitable Grade Level
Grades 10-12
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