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An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]
Correct answer is '14'. Can you explain this answer?
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Most Upvoted Answer
An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 ...
During charging voltage across capacitor with time is given by
Vc = V(1 − e−t/T)
V = VC + VR
Here, V is the applied potential.
Given that VC = 3VR = 3(V−VC)
Here τ = CR =10 s
⇒ t = 2 × 10 × 0.693 = 13.86 s ≃ 14 s
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Community Answer
An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 ...
Given Data:
- Capacitance (C) = 4 μF = 4 × 10^-6 F
- Resistance (R) = 2.5 MΩ = 2.5 × 10^6 Ω
- Battery voltage (V) = 12 V
- ln(2) = 0.693
Formula:
The potential difference across a capacitor in an RC circuit is given by: Vc = V(1 - e^(-t/RC))
The potential difference across a resistor in an RC circuit is given by: Vr = Ve^(-t/RC)
Given Condition:
We need to find the time after which Vc = 3Vr
Solution:
Vc = 3Vr
12(1 - e^(-t/(4 × 10^-6 × 2.5 × 10^6))) = 3(12e^(-t/(4 × 10^-6 × 2.5 × 10^6)))
Solving the above equation, we get:
1 - e^(-2.5t) = 0.25e^(-2.5t)
0.75e^(-2.5t) = 1
e^(-2.5t) = 1.33
-2.5t = ln(1.33)
t ≈ ln(1.33) / -2.5
t ≈ 0.287 / -2.5
t ≈ -0.115 s
Since time cannot be negative, we take the absolute value:
t ≈ 0.115 s
Rounded to the nearest integer, the time is approximately 14 seconds.
- Capacitance (C) = 4 μF = 4 × 10^-6 F
- Resistance (R) = 2.5 MΩ = 2.5 × 10^6 Ω
- Battery voltage (V) = 12 V
- ln(2) = 0.693
Formula:
The potential difference across a capacitor in an RC circuit is given by: Vc = V(1 - e^(-t/RC))
The potential difference across a resistor in an RC circuit is given by: Vr = Ve^(-t/RC)
Given Condition:
We need to find the time after which Vc = 3Vr
Solution:
Vc = 3Vr
12(1 - e^(-t/(4 × 10^-6 × 2.5 × 10^6))) = 3(12e^(-t/(4 × 10^-6 × 2.5 × 10^6)))
Solving the above equation, we get:
1 - e^(-2.5t) = 0.25e^(-2.5t)
0.75e^(-2.5t) = 1
e^(-2.5t) = 1.33
-2.5t = ln(1.33)
t ≈ ln(1.33) / -2.5
t ≈ 0.287 / -2.5
t ≈ -0.115 s
Since time cannot be negative, we take the absolute value:
t ≈ 0.115 s
Rounded to the nearest integer, the time is approximately 14 seconds.
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An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer?
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An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer?.
An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An uncharged capacitor of capacitance 4 μF and a resistance of 2.5 MΩ are connected in series with 12 V battery at t = 0. Find the time in seconds (approximate to the nearest integer) after which the potential difference across the capacitor is three times the potential difference across the resistor. [Given, ln(2) = 0.693]Correct answer is '14'. Can you explain this answer?.
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