Find the total energy stored in the circuit? + 3 L = 2 mH %3D L= 4 mH %3D m C = 20 µF C2 = 50 µFP %3D 9V(+ 360 ЗА +

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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The image presents an electrical circuit with the task: "Find the total energy stored in the circuit?"

**Circuit Components:**

1. **Voltage Source:**
   - A 9V battery supplies power to the circuit.

2. **Resistors:**
   - There are three resistors. Two are labeled as 6Ω each, and one is 3Ω.

3. **Inductors:**
   - Inductor \(L_1\) with an inductance of 2 mH.
   - Inductor \(L_2\) with an inductance of 4 mH.

4. **Capacitors:**
   - Capacitor \(C_1\) with a capacitance of 20 μF.
   - Capacitor \(C_2\) with a capacitance of 50 μF.

5. **Current Source:**
   - A 3A current source is present in the circuit.

**Annotations:**

- The circuit diagram includes red annotations indicating the direction of the current flow and markings for voltage polarity on the capacitors.
- The total inductance \(L_1 + L_2\) is noted in the red annotations as a reminder for calculations.

**Objective:**

Calculate the total energy stored in the capacitors and inductors of the circuit.

**Energy Calculations:**

1. **Energy Stored in Capacitors:**
   - Formula: \( E_C = \frac{1}{2} C V^2 \)
   - Calculate separately for \(C_1\) and \(C_2\) using their respective capacitance values and voltage.

2. **Energy Stored in Inductors:**
   - Formula: \( E_L = \frac{1}{2} L I^2 \)
   - Calculate separately for \(L_1\) and \(L_2\) using their respective inductance values and current.

Sum the energies to find the total energy stored in the circuit.
Transcribed Image Text:The image presents an electrical circuit with the task: "Find the total energy stored in the circuit?" **Circuit Components:** 1. **Voltage Source:** - A 9V battery supplies power to the circuit. 2. **Resistors:** - There are three resistors. Two are labeled as 6Ω each, and one is 3Ω. 3. **Inductors:** - Inductor \(L_1\) with an inductance of 2 mH. - Inductor \(L_2\) with an inductance of 4 mH. 4. **Capacitors:** - Capacitor \(C_1\) with a capacitance of 20 μF. - Capacitor \(C_2\) with a capacitance of 50 μF. 5. **Current Source:** - A 3A current source is present in the circuit. **Annotations:** - The circuit diagram includes red annotations indicating the direction of the current flow and markings for voltage polarity on the capacitors. - The total inductance \(L_1 + L_2\) is noted in the red annotations as a reminder for calculations. **Objective:** Calculate the total energy stored in the capacitors and inductors of the circuit. **Energy Calculations:** 1. **Energy Stored in Capacitors:** - Formula: \( E_C = \frac{1}{2} C V^2 \) - Calculate separately for \(C_1\) and \(C_2\) using their respective capacitance values and voltage. 2. **Energy Stored in Inductors:** - Formula: \( E_L = \frac{1}{2} L I^2 \) - Calculate separately for \(L_1\) and \(L_2\) using their respective inductance values and current. Sum the energies to find the total energy stored in the circuit.
Expert Solution
Step 1 Concept

Capacitor circuit : In many practical circuits, the steady-state is reached fast if the current at each point in the circuit remains constant (i.e., it does not change with time) as shown in the diagram. Any charge (or current) that enters the circuit must equal the charge (or current) that leaves it. A capacitor is an electrical component that absorbs and stores energy from a battery. The terminals are connected to two metal plates on the inside, which are separated by a non-conducting material. When a capacitor is engaged, it swiftly releases electricity in a fraction of a second.

Inductor in a circuit : Inductors are commonly employed in switched-mode power systems to produce DC current as energy storage devices. The inductor stores energy and delivers it to the circuit to keep current flowing during "off" switching periods, allowing for topographies with output voltage exceeding input voltage. Inductors are devices that store energy. The magnetic field begins to collapse and release energy as the current is gradually reduced, and the inductor becomes a current source. The inductor stores and delivers energy continuously when an alternating current (AC) flows through it.

 

 

 

 

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