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For the RC parallel circuit, determine the voltage across the capacitor using Laplace transform, assume capacitor is initially relaxed.
- a)50(1 − e−t/5)
- b)50(1 + e−t/5)
- c)5(1 − e−t/5)
- d)5(1 + e−t/5)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For the RC parallel circuit, determine the voltage across the capacito...
Concept:
If V0 is the initial voltage across capacitor
Calculation:
Circuit diagram at laplace domain
As capacitor was initially relaxed: V0 = 0 (Voltage source will be replaced by a short circuit)
Given;
C = 1μF
R= 5 Ω
Use nodal analysis at node VC
⇒ VC/R + VC/(1/sC) = 10/s
⇒ VC( 1/R + sC) = 10/s
⇒ VC( 1+ sRC)/R = 10/s
⇒ VC= 10R/s( 1+ sRC)
⇒ VC= 10R/sRC( 1/RC+ s)
⇒ VC= (10/C)/s( s+ 1/RC)
⇒ VC = A/s + B/(s + 1/RC)
Determine the values of A and B using partial fraction
As=0 = (10/C)/(s + 1/RC) = (10/C)( 0 +1/RC) = 10R
Bs= -1/RC = (10/C)/s = -10R
⇒ VC = (10R)/s + (-10R)/(s + 1/RC)
Using inverse laplace transform:
⇒ VC = 10R -10Re-t/RC
⇒ VC = 10R(1 -e-t/RC)
∴ VC = 50(1 - e-t/5)
Most Upvoted Answer
For the RC parallel circuit, determine the voltage across the capacito...
Concept:
If V0 is the initial voltage across capacitor
Calculation:
Circuit diagram at laplace domain
As capacitor was initially relaxed: V0 = 0 (Voltage source will be replaced by a short circuit)
Given;
C = 1μF
R= 5 Ω
Use nodal analysis at node VC
⇒ VC/R + VC/(1/sC) = 10/s
⇒ VC( 1/R + sC) = 10/s
⇒ VC( 1+ sRC)/R = 10/s
⇒ VC= 10R/s( 1+ sRC)
⇒ VC= 10R/sRC( 1/RC+ s)
⇒ VC= (10/C)/s( s+ 1/RC)
⇒ VC = A/s + B/(s + 1/RC)
Determine the values of A and B using partial fraction
As=0 = (10/C)/(s + 1/RC) = (10/C)( 0 +1/RC) = 10R
Bs= -1/RC = (10/C)/s = -10R
⇒ VC = (10R)/s + (-10R)/(s + 1/RC)
Using inverse laplace transform:
⇒ VC = 10R -10Re-t/RC
⇒ VC = 10R(1 -e-t/RC)
∴ VC = 50(1 - e-t/5)
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For the RC parallel circuit, determine the voltage across the capacitor using Laplace transform, assume capacitor is initially relaxed.a)50(1 − e−t/5)b)50(1 + e−t/5)c)5(1 − e−t/5)d)5(1 + e−t/5)Correct answer is option 'A'. Can you explain this answer?
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