In the circuit shown in Fig. XC = 100 , XL =200 and R = 100 . The effective currentthrough the source is

1. Break Down the Problem

To find the effective current through the source, we need to consider the components in the circuit:

• XC (capacitive reactance) = 100 Ω
• XL (inductive reactance) = 200 Ω
• R (resistance) = 100 Ω

The next step is to determine the total impedance (Z) of the circuit.

2. Relevant Concepts

The total impedance $Z$ in an RLC circuit (where components are in series) can be calculated with the formula: $Z = R + j(X_L - X_C)$ Where:

• $R$ is the resistance
• $X_L$ is the inductive reactance
• $X_C$ is the capacitive reactance
• $j$ is the imaginary unit (used to represent phase differences)

3. Analysis and Detail

1. Calculate the net reactance: $X_L - X_C = 200\, \Omega - 100\, \Omega = 100\, \Omega$

2. Calculate the total impedance: $Z = R + j(X_L - X_C) = 100\, \Omega + j(100\, \Omega)$

3. Calculate the magnitude of the impedance: $|Z| = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{(100)^2 + (100)^2} = \sqrt{10000 + 10000} = \sqrt{20000} = 141.42\, \Omega$

4. Verify and Summarize

Now, if we assume the voltage $V$ across the source (not given in the problem), the effective current $I$ can be calculated using Ohm's Law: $I = \frac{V}{|Z|}$ Without a specific voltage value, we summarize the current as: $I = \frac{V}{141.42}$ Thus, the effective current through the source depends on the applied voltage across these components.

Final Answer

The effective current through the source can be represented as: $I = \frac{V}{141.42\, \Omega}$ where $V$ is the applied voltage across the circuit.