### Transcription for Educational Website**Section: Capacitor Circuits****Problem 9.35: Analyzing a Capacitor Circuit**A current \( i(t) \) is applied to a capacitor of \( C = 100 \, \mu F \), as shown in the Figure 9.35.**Figure P9.35: Diagram and Graph**1. **Diagram:** The left portion of Figure P9.35 illustrates a simple circuit with a capacitor, \( C \), in parallel with a voltage \( v(t) \). The current source \( i(t) \) is applied to this circuit.2. **Graph:** The right portion of Figure P9.35 presents a graph of the current \( i(t) \) in milliamperes (mA) over time \( t \) in milliseconds (ms). The graph can be described as follows: - From \( t = 0 \) to \( t = 1 \, \text{ms} \), the current \( i(t) \) is constant at 100 mA. - From \( t = 1 \, \text{ms} \) to \( t = 2 \, \text{ms} \), the current drops to 0 mA. - From \( t = 2 \, \text{ms} \) to \( t = 3 \, \text{ms} \), the current increases to 50 mA. - From \( t = 3 \, \text{ms} \) to \( t = 4 \, \text{ms} \), the current decreases to -50 mA.**Task:**(a) Knowing that \( i(t) = C \frac{dv(t)}{dt} \), sketch the voltage across the capacitor \( v(t) \).**Explanation:**The graph suggests changes in the current over discrete time intervals, which will affect the voltage \( v(t) \) as per the relationship \( i(t) = C \frac{dv(t)}{dt} \). Analyze how the variations in \( i(t) \) will affect the voltage \( v(t) \) using integration over each time interval. **Instructions:**Assume \( v(0) = 0 \, \text{V} \). Also note that the time \( t \) is measured in milliseconds (ms) and the current \( i(t) \) is measured in milliamperes (mA).(b) Given the results of part (a), sketch the power \( p(t) = v(t)i(t) \).**Explanation:**The task involves sketching the power \( p(t) \), assuming that \( v(t) \) is a known function of time. The power is calculated by multiplying the voltage \( v(t) \) by the current \( i(t) \). Ensure the units of measurement for time and current are correctly applied in your calculations or sketches.

Answered: Image /qna-images/answer/53705490-fe4e-4322-a7e8-4bdd2a894008.jpg

5. A current i(t) is applied to a capa- citor of C = 100 µF, as shown in the Figure 9.35. %3D i(1) (mA) 100 50 tv(r) 0. (ms) -50- 100 igure P9.35 A current applied to a 100 µF apacitor. (a) Knowing that i(t) = Cdv, sketch the voltage across the capacitor v(1). %3D di Wowe

5. A current i(t) is applied to a capa- citor of C = 100 µF, as shown in the Figure 9.35. %3D i(1) (mA) 100 50 tv(r) 0. (ms) -50- 100 igure P9.35 A current applied to a 100 µF apacitor. (a) Knowing that i(t) = Cdv, sketch the voltage across the capacitor v(1). %3D di Wowe

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).

Question

### Transcription for Educational Website

**Section: Capacitor Circuits**

**Problem 9.35: Analyzing a Capacitor Circuit**

A current \( i(t) \) is applied to a capacitor of \( C = 100 \, \mu F \), as shown in the Figure 9.35.

**Figure P9.35: Diagram and Graph**

1. **Diagram:** The left portion of Figure P9.35 illustrates a simple circuit with a capacitor, \( C \), in parallel with a voltage \( v(t) \). The current source \( i(t) \) is applied to this circuit.

2. **Graph:** The right portion of Figure P9.35 presents a graph of the current \( i(t) \) in milliamperes (mA) over time \( t \) in milliseconds (ms). The graph can be described as follows:
- From \( t = 0 \) to \( t = 1 \, \text{ms} \), the current \( i(t) \) is constant at 100 mA.
- From \( t = 1 \, \text{ms} \) to \( t = 2 \, \text{ms} \), the current drops to 0 mA.
- From \( t = 2 \, \text{ms} \) to \( t = 3 \, \text{ms} \), the current increases to 50 mA.
- From \( t = 3 \, \text{ms} \) to \( t = 4 \, \text{ms} \), the current decreases to -50 mA.

**Task:**

(a) Knowing that \( i(t) = C \frac{dv(t)}{dt} \), sketch the voltage across the capacitor \( v(t) \).

**Explanation:**

The graph suggests changes in the current over discrete time intervals, which will affect the voltage \( v(t) \) as per the relationship \( i(t) = C \frac{dv(t)}{dt} \). Analyze how the variations in \( i(t) \) will affect the voltage \( v(t) \) using integration over each time interval.

**Instructions:**

Assume \( v(0) = 0 \, \text{V} \). Also note that the time \( t \) is measured in milliseconds (ms) and the current \( i(t) \) is measured in milliamperes (mA).

(b) Given the results of part (a), sketch the power \( p(t) = v(t)i(t) \).

**Explanation:**

The task involves sketching the power \( p(t) \), assuming that \( v(t) \) is a known function of time. The power is calculated by multiplying the voltage \( v(t) \) by the current \( i(t) \). Ensure the units of measurement for time and current are correctly applied in your calculations or sketches.

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