Find Zequ for the given circuit in Fig.3 and use that to find current I. Let w= 10 rad/sec

To solve the problem of finding the equivalent impedance $Z_{equ}$ for the given circuit and subsequently calculating the current $I$ with an angular frequency $\omega = 10 \, \text{rad/sec}$, we will proceed with the following steps:

1. Break Down the Problem

1. Identify the components in the circuit (resistors, capacitors, inductors) and their configurations (series or parallel).
2. Determine the impedance of each component at the given frequency.
3. Calculate the equivalent impedance $Z_{equ}$ of the circuit.
4. Use $Z_{equ}$ to find the current $I$ using Ohm's Law.

2. Relevant Concepts

1. Impedance of a resistor $R$: $Z_R = R$

2. Impedance of a capacitor $C$: $Z_C = \frac{1}{j\omega C}$

3. Impedance of an inductor $L$: $Z_L = j\omega L$

4. Ohm's Law: $I = \frac{V}{Z_{equ}}$

3. Analysis and Detail

1. Identify Components:

   • Assume we have given values for $R$, $C$, and $L$ (not provided, so you would need to substitute these with real values).

2. Calculate Impedance:

   • For resistor $R$, the impedance is: $Z_R = R$

   • For capacitor $C$: $Z_C = \frac{1}{j(10)C}$

   • For inductor $L$: $Z_L = j(10)L$

3. Combine Impedances:

   • If the components are in series: $Z_{equ} = Z_R + Z_C + Z_L$

   • If in parallel, use: $\frac{1}{Z_{equ}} = \frac{1}{Z_R} + \frac{1}{Z_C} + \frac{1}{Z_L}$

4. Calculate Current:

   • Using Ohm's Law to find $I$: $I = \frac{V}{Z_{equ}}$
   • Substitute the voltage $V$ (not provided, so use your specific value).

4. Verify and Summarize

• Verify all calculations and ensure correct use of complex numbers.
• Summarize the equivalent impedance $Z_{equ}$ and the resulting current $I$.

Final Answer

Once you've substituted in your specific values for $R$, $C$, $L$, and $V$, you can compute $Z_{equ}$ and $I$. Without specific values, the formulas remain generalized as:

$Z_{equ} = \text{(expression depending on series or parallel configurations)}$ $I = \frac{V}{Z_{equ}}$