Math Problem Statement

الشكل المرفق يعبر عن دائرة RLC عند تردد معين، فإن قيمة التيار المار بالدائرة تساوي؟

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:

Z=R2+(XLXC)2Z = \sqrt{R^2 + \left( X_L - X_C \right)^2} Where:

  • XL=2πfLX_L = 2\pi f L is the inductive reactance
  • XC=12πfCX_C = \frac{1}{2\pi f C} is the capacitive reactance

Once we calculate ZZ, the current II is given by:

I=VZI = \frac{V}{Z}

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