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A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).
Correct answer is '54.99'. Can you explain this answer?
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Verified Answer
A resistor and a capacitor are connected in series to a 10 V dc supply...
If initial charge polarities on the capacitor is opposite to the supply voltage then only the capacitor voltage crosses the zero line.
Vc(t) ⇒ Final value + (Initial value – Final value) e–t/τ
0 = 10 + (–V0 – 10) e–0.4
10 = (V0 + 10) e–0.4
V0 = 4.918 V
Now, t =0.2τ
%change in voltage =
Vc(t) ⇒ Final value + (Initial value – Final value) e–t/τ
0 = 10 + (–V0 – 10) e–0.4
10 = (V0 + 10) e–0.4
V0 = 4.918 V
Now, t =0.2τ
%change in voltage =
Most Upvoted Answer
A resistor and a capacitor are connected in series to a 10 V dc supply...
To find the time constant (τ) of the circuit, we can use the formula:
τ = R * C
where R is the resistance and C is the capacitance.
Since the capacitor voltage crosses 0 V at t = 0.4, we can say that the time constant (τ) is equal to 0.4 seconds.
Now, let's consider the circuit equation for the voltage across the capacitor (Vc):
Vc = V * (1 - e^(-t/τ))
where V is the supply voltage (10 V), t is the time, and e is the base of natural logarithm.
Since the switch is closed at t = 0, the voltage across the capacitor at t = 0 is 0 V. Therefore, we can write:
0 = 10 * (1 - e^(-0/τ))
0 = 10 * (1 - e^0)
0 = 10 * (1 - 1)
0 = 10 * 0
This equation is not satisfied, which means that there is an error in the given information. The voltage across the capacitor cannot be 0 V at t = 0.4 if the switch is closed at t = 0 and the capacitor is initially uncharged.
τ = R * C
where R is the resistance and C is the capacitance.
Since the capacitor voltage crosses 0 V at t = 0.4, we can say that the time constant (τ) is equal to 0.4 seconds.
Now, let's consider the circuit equation for the voltage across the capacitor (Vc):
Vc = V * (1 - e^(-t/τ))
where V is the supply voltage (10 V), t is the time, and e is the base of natural logarithm.
Since the switch is closed at t = 0, the voltage across the capacitor at t = 0 is 0 V. Therefore, we can write:
0 = 10 * (1 - e^(-0/τ))
0 = 10 * (1 - e^0)
0 = 10 * (1 - 1)
0 = 10 * 0
This equation is not satisfied, which means that there is an error in the given information. The voltage across the capacitor cannot be 0 V at t = 0.4 if the switch is closed at t = 0 and the capacitor is initially uncharged.
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A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer?
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A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer?.
A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer?.
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A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer?, a detailed solution for A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? has been provided alongside types of A resistor and a capacitor are connected in series to a 10 V dc supply through a switch.The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossings has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).Correct answer is '54.99'. Can you explain this answer? theory, EduRev gives you an
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