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2. The expression for capacitor voltage in an RC circuit (assuming no initial charge) when DC voltage is applied is vc(t) = V,(1 – e-(t/RC)). Assume V; = 10 V, C= 50 µF, and R = 100 2. Calculate capacitor voltage when t= : 1*RC 5*RC 10*RC 3. The voltage across an inductor when a DC voltage is switched on is v(t) = Ve-(t/[L/R]). Assume V, = 10 V, L =1 mH, and R= 1 Q. Find the voltage across the capacitor at t = : 0 ms 1 ms 10 ms

2. The expression for capacitor voltage in an RC circuit (assuming no initial charge) when DC voltage is applied is vc(t) = V,(1 – e-(t/RC)). Assume V; = 10 V, C= 50 µF, and R = 100 2. Calculate capacitor voltage when t= : 1*RC 5*RC 10*RC 3. The voltage across an inductor when a DC voltage is switched on is v(t) = Ve-(t/[L/R]). Assume V, = 10 V, L =1 mH, and R= 1 Q. Find the voltage across the capacitor at t = : 0 ms 1 ms 10 ms

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
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Please help me answer question 1. 2. And 3. The bottom paragraph. 

**2. Problem Statement:** The expression for capacitor voltage in an RC circuit (assuming no initial charge) when DC voltage is applied is given by: \[ v_c(t) = V_s \left(1 - e^{-(t/RC)}\right) \] Assume \( V_s = 10 \, \text{V} \), \( C = 50 \, \mu\text{F} \), and \( R = 100 \, \Omega \). Calculate capacitor voltage when \( t = \): - \( 1 \times RC \) _______________ - \( 5 \times RC \) _______________ - \( 10 \times RC \) _______________ **3. Problem Statement:** The voltage across an inductor when a DC voltage is switched on is given by: \[ v_L(t) = V e^{-(t/[L/R])} \] Assume \( V_s = 10 \, \text{V} \), \( L = 1 \, \text{mH} \), and \( R = 1 \, \Omega \). Find the voltage across the capacitor at \( t = \): - \( 0 \, \text{ms} \) _______________ - \( 1 \, \text{ms} \) _______________ - \( 10 \, \text{ms} \) _______________ **4. Derivation:** Consider the equation for \(\omega_d\): \[ \omega_d = \sqrt{\left(\frac{1}{LC}\right) - \left(\frac{R}{2L}\right)^2} \] Oscillation will occur only when this expression is a real number (not an imaginary number). Solving, we see that the expression is a real number when: \[ \left(\frac{1}{LC}\right) > \left(\frac{R}{2L}\right)^2 \] If \( C = 0.01 \, \mu\text{F} \) capacitance and \( L = 10 \, \text{mH} \), what is the largest value of \( R \) for this condition to be true? You will use this result in the lab.
Transcribed Image Text:**2. Problem Statement:** The expression for capacitor voltage in an RC circuit (assuming no initial charge) when DC voltage is applied is given by: \[ v_c(t) = V_s \left(1 - e^{-(t/RC)}\right) \] Assume \( V_s = 10 \, \text{V} \), \( C = 50 \, \mu\text{F} \), and \( R = 100 \, \Omega \). Calculate capacitor voltage when \( t = \): - \( 1 \times RC \) _______________ - \( 5 \times RC \) _______________ - \( 10 \times RC \) _______________ **3. Problem Statement:** The voltage across an inductor when a DC voltage is switched on is given by: \[ v_L(t) = V e^{-(t/[L/R])} \] Assume \( V_s = 10 \, \text{V} \), \( L = 1 \, \text{mH} \), and \( R = 1 \, \Omega \). Find the voltage across the capacitor at \( t = \): - \( 0 \, \text{ms} \) _______________ - \( 1 \, \text{ms} \) _______________ - \( 10 \, \text{ms} \) _______________ **4. Derivation:** Consider the equation for \(\omega_d\): \[ \omega_d = \sqrt{\left(\frac{1}{LC}\right) - \left(\frac{R}{2L}\right)^2} \] Oscillation will occur only when this expression is a real number (not an imaginary number). Solving, we see that the expression is a real number when: \[ \left(\frac{1}{LC}\right) > \left(\frac{R}{2L}\right)^2 \] If \( C = 0.01 \, \mu\text{F} \) capacitance and \( L = 10 \, \text{mH} \), what is the largest value of \( R \) for this condition to be true? You will use this result in the lab.
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