a coin inductance 159.2 Milli Henry and resistance 20 ohm is connected in serieswith 60 ohm ressistant to A 240 volt and 50Hz supply determine,A imped of circuit circuit

Let's solve for the impedance of the circuit. 

Given dataLet's solve for the impedance of the circuit. 

Given 
- Inductance, \( L = 159.2 \ \text{mH} = 0.1592 \ \text{H} \)
- Resistance of the inductor, \( R_L = 20 \ \Omega \)
- Series resistance, \( R_s = 60 \ \Omega \)
- Voltage, \( V = 240 \ \text{V} \)
- Frequency, \( f = 50 \ \text{Hz} \)

### Step 1: Calculate the inductive reactance \( X_L \)
Inductive reactance is given by the formula:
\[
X_L = 2 \pi f L
\]
where:
- \( f \) is the frequency,
- \( L \) is the inductance.

### Step 2: Determine total impedance \( Z \)
The total impedance for a series circuit is the square root of the sum of squares of the total resistance and the inductive reactance:
\[
Z = \sqrt{(R_{\text{total}})^2 + X_L^2}
\]
where:
- \( R_{\text{total}} = R_L + R_s \).

Let me calculate this for you.The impedance of the circuit is approximately \( 94.35 \ \Omega \).

Would you like any further details on this, or do you have any questions?

Here are five related questions to expand on this topic:
1. How does the frequency affect the inductive reactance of the circuit?
2. What is the phase angle between the voltage and current in this circuit?
3. How would the impedance change if the inductance was halved?
4. How does adding a capacitor in parallel with the inductor impact the total impedance?
5. How do you calculate the current through the circuit given the impedance?

**Tip:** Always ensure the units of inductance, capacitance, and resistance are consistent before performing calculations in AC circuits.

Learn how to calculate the impedance of a series AC circuit containing an inductor, resistors, and a specified voltage and frequency. This detailed solution includes step-by-step calculations for inductive reactance and total impedance. Suitable for advanced learners and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation