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4. In the circuit below, the voltage Ved(t) = 25 cos(377t + 45°) V. i(t) Vo(t) 10k2 0.2uF d. a) Find the admittance of the circuit. b) Draw a phasor diagram showing the current in each element, the voltage Ved, and the phasor current I corresponding to i(t).

4. In the circuit below, the voltage Ved(t) = 25 cos(377t + 45°) V. i(t) Vo(t) 10k2 0.2uF d. a) Find the admittance of the circuit. b) Draw a phasor diagram showing the current in each element, the voltage Ved, and the phasor current I corresponding to i(t).

Introductory Circuit Analysis (13th Edition)
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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Attached is the file for the formula sheet. Please answer all parts
**Problem Statement:** 4. In the circuit below, the voltage \( V_{cd}(t) = 25 \cos(377t + 45^\circ) \) V. **Circuit Description:** - The circuit consists of a resistor and a capacitor in series. - The resistor has a resistance of \(10 \, \text{k}\Omega\). - The capacitor has a capacitance of \(0.2 \, \mu\text{F}\). - The voltage source \( V_{cd}(t) \) is applied across points \( c \) and \( d \). - The current flowing through the circuit is denoted as \( i(t) \). **Tasks:** a) Find the admittance of the circuit. b) Draw a phasor diagram showing the current in each element, the voltage \( V_{cd} \), and the phasor current \( I \) corresponding to \( i(t) \).
Transcribed Image Text:**Problem Statement:** 4. In the circuit below, the voltage \( V_{cd}(t) = 25 \cos(377t + 45^\circ) \) V. **Circuit Description:** - The circuit consists of a resistor and a capacitor in series. - The resistor has a resistance of \(10 \, \text{k}\Omega\). - The capacitor has a capacitance of \(0.2 \, \mu\text{F}\). - The voltage source \( V_{cd}(t) \) is applied across points \( c \) and \( d \). - The current flowing through the circuit is denoted as \( i(t) \). **Tasks:** a) Find the admittance of the circuit. b) Draw a phasor diagram showing the current in each element, the voltage \( V_{cd} \), and the phasor current \( I \) corresponding to \( i(t) \).
**Formulas:** - \(\omega = 2 \times \pi \times f\) - \(A \cos(\omega t + \theta) \rightarrow A \angle \theta\) - \(V = I \times Z\) - **Polar to rectangular:** - Polar: \(R \angle \theta\) - \(a = R \times \sin \theta\) - \(b = R \times \cos \theta\) **Rectangular: \(a + jb\)** - **Rectangular to polar:** - Rectangular: \(a + jb\) - \(R = \sqrt{a^2 + b^2}\) - \(\theta = \tan^{-1}\frac{b}{a}\) **Polar: \(R \angle \theta\)** --- **Component Table:** | Component | Value | Reactance (X) | Impedance Z (Rectangular) | Impedance Z (Polar) | |-----------|-------|---------------|---------------------------|---------------------| | Resistor | \(R\) | \(R\) | \(R + 0j\) | \(R \angle 0\) | | Capacitor | \(C\) | \(1/\omega C\) or \(1/2\pi f C\) | \(1/j\omega C\) or \(-j/\omega C\) | \(1/\omega C \angle -90^\circ\) | | Inductor | \(L\) | \(\omega L\) or \(2\pi f L\) | \(j\omega L\) | \(\omega L \angle 90^\circ\) | --- - **Admittance \(Y = \frac{1}{\text{Impedance } Z}\)** - Always draw impedance phasors with reference as resistor impedance. For example, if you have a 200 ohm resistor, an inductor with impedance of 100 ohms, and capacitor with impedance of 1000 ohms: - Phasor diagram explanation: - The vector on the right represents a resistor with an impedance of \(200 \angle 0^\circ\). - The upward vector represents an inductor with an impedance of \(100 \angle 90^\circ\). - The downward
Transcribed Image Text:**Formulas:** - \(\omega = 2 \times \pi \times f\) - \(A \cos(\omega t + \theta) \rightarrow A \angle \theta\) - \(V = I \times Z\) - **Polar to rectangular:** - Polar: \(R \angle \theta\) - \(a = R \times \sin \theta\) - \(b = R \times \cos \theta\) **Rectangular: \(a + jb\)** - **Rectangular to polar:** - Rectangular: \(a + jb\) - \(R = \sqrt{a^2 + b^2}\) - \(\theta = \tan^{-1}\frac{b}{a}\) **Polar: \(R \angle \theta\)** --- **Component Table:** | Component | Value | Reactance (X) | Impedance Z (Rectangular) | Impedance Z (Polar) | |-----------|-------|---------------|---------------------------|---------------------| | Resistor | \(R\) | \(R\) | \(R + 0j\) | \(R \angle 0\) | | Capacitor | \(C\) | \(1/\omega C\) or \(1/2\pi f C\) | \(1/j\omega C\) or \(-j/\omega C\) | \(1/\omega C \angle -90^\circ\) | | Inductor | \(L\) | \(\omega L\) or \(2\pi f L\) | \(j\omega L\) | \(\omega L \angle 90^\circ\) | --- - **Admittance \(Y = \frac{1}{\text{Impedance } Z}\)** - Always draw impedance phasors with reference as resistor impedance. For example, if you have a 200 ohm resistor, an inductor with impedance of 100 ohms, and capacitor with impedance of 1000 ohms: - Phasor diagram explanation: - The vector on the right represents a resistor with an impedance of \(200 \angle 0^\circ\). - The upward vector represents an inductor with an impedance of \(100 \angle 90^\circ\). - The downward
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