3- For the R-C circuit, Determine the time constant for the following circuit when the switch is thrown into position 1. b). Plot the wave forms for Nc andic For the switch in position 1. cli Plot the wavefor for va and ie for the switch in position 2. ic 24 1K
3- For the R-C circuit, Determine the time constant for the following circuit when the switch is thrown into position 1. b). Plot the wave forms for Nc andic For the switch in position 1. cli Plot the wavefor for va and ie for the switch in position 2. ic 24 1K
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter25: Surge, Spike, And Lightning Protection
Section: Chapter Questions
Problem 10RQ: In reference to the load, how are capacitors connected to help prevent voltage spikes and surges?...
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Question
```
+----o---- 1kΩ ----+
| |
| |
5V ---o-- 1kΩ --+ |
| | |
+-- 2µF --+--o----+
(C) (Position 1)
```
### Explanation:
1. **Time Constant Calculation (Part a):**
The time constant (\( \tau \)) of an R-C circuit is given by:
\[
\tau = R \cdot C
\]
For the given circuit, where \( R = 1kΩ \) and \( C = 2μF \):
\[
\tau = 1000Ω \cdot 2 \times 10^{-6}F = 2 \times 10^{-3} \text{ seconds} = 2 \text{ ms}
\]
2. **Waveforms with Switch in Position 1 (Part b):**
When the switch is in position 1, the capacitor will charge through the 1kΩ resistor and the 5V supply.
- **Voltage across the capacitor \( v_C(t) \):**
\[
v_C(t) = V_s \left( 1 - e^{-\frac{t}{\tau}} \right)
\]
Where \( V_s = 5V \).
- **Current through the capacitor \( i_C(t) \):**
\[
i_C(t) = \frac{V_s}{R} e^{-\frac{t}{\tau}}
\]
Where \( \frac{V_s}{R} = \frac{5V}{1kΩ} = 5 \times 10^{-3} \text{ A} = 5mA \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2405e5cb-20d1-4277-a72a-e2ca429d5d5b%2Fd52d2f93-9b88-4a8d-a811-9e9db698feeb%2Fi4t78b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### R-C Circuit Analysis
**Problem:**
Given the R-C circuit shown, perform the following analyses:
**a) Determine the time constant for the circuit when the switch is thrown into position 1.**
**b) Plot the waveforms for \( v_C \) and \( i_C \) for the switch in position 1.**
**c) Plot the waveforms for \( v_C \) and \( i_C \) for the switch in position 2.**
### Circuit Diagram:
```
+----o---- 1kΩ ----+
| |
| |
5V ---o-- 1kΩ --+ |
| | |
+-- 2µF --+--o----+
(C) (Position 1)
```
### Explanation:
1. **Time Constant Calculation (Part a):**
The time constant (\( \tau \)) of an R-C circuit is given by:
\[
\tau = R \cdot C
\]
For the given circuit, where \( R = 1kΩ \) and \( C = 2μF \):
\[
\tau = 1000Ω \cdot 2 \times 10^{-6}F = 2 \times 10^{-3} \text{ seconds} = 2 \text{ ms}
\]
2. **Waveforms with Switch in Position 1 (Part b):**
When the switch is in position 1, the capacitor will charge through the 1kΩ resistor and the 5V supply.
- **Voltage across the capacitor \( v_C(t) \):**
\[
v_C(t) = V_s \left( 1 - e^{-\frac{t}{\tau}} \right)
\]
Where \( V_s = 5V \).
- **Current through the capacitor \( i_C(t) \):**
\[
i_C(t) = \frac{V_s}{R} e^{-\frac{t}{\tau}}
\]
Where \( \frac{V_s}{R} = \frac{5V}{1kΩ} = 5 \times 10^{-3} \text{ A} = 5mA \
Transcribed Image Text:**Title: Reducing Electrical Circuit to the Fewest Elements**
**Introduction:**
In this exercise, you will learn how to simplify a given electrical circuit to its fewest elements. Simplification of circuits helps in analyzing the circuit more easily and ensures efficient performance.
**Step 4: Reduce to the Fewest Elements**
**Circuit Diagram Explanation:**
1. **Capacitors in a Bridge Arrangement:**
- The circuit starts with a bridge arrangement consisting of four capacitors.
- Top left capacitor: 5 pF (picoFarads)
- Top right capacitor: 5 pF
- Bottom left capacitor: 10 pF
- Bottom right capacitor: 10 pF
2. **Resistor:**
- Following the bridge circuit, there is a resistor with a resistance of 10 kΩ (kiloOhms).
3. **Inductors in Parallel:**
- There is a series of inductors arranged in parallel after the resistor.
- Left inductor: 5 mH (milliHenries)
- Top middle inductor: 3 mH
- Bottom middle inductor: 2 mH
- Right inductor: 5 mH
**Tasks:**
- Your goal is to combine and simplify this circuit by reducing it to the fewest possible elements. When simplifying, perform the following steps:
1. **Combine capacitors in the bridge arrangement** to a single equivalent capacitor.
2. **Combine inductors in the parallel arrangement** to form a single equivalent inductor.
**Important Notes:**
- You may need to use formulas for combining series and parallel capacitors and inductors.
- Ensure all units are consistent when performing calculations.
This exercise aims to illustrate the importance of circuit simplification for better analysis and understanding of circuit behavior.
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Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning