SATHEE: Electrostatics 6 Question 3

Electrostatics 6 Question 3

3. A $4 μ F$ capacitor and a resistance of $2.5 M Ω$ are in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, $\ln (2) = 0.693$ ]

(2005, 2M)

(a) $13.86 s$

(b) $6.93 s$

(d) $14 s$

$(1983, 6 M)$

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Answer:

Correct Answer: 3. (a)

Solution:

Given : $V_{C} = 3 V_{R} = 3 (V - V_{C})$

Here, $V$ is the applied potential.

$\begin{array}{ll} ∴ & V_{C} = \frac{3}{4} V or V (1 - e^{- t / τ_{c}}) = \frac{3}{4} V \\ ∴ & e^{- t / τ_{c}} = \frac{1}{4} \end{array}$

Here,

$τ_{c} = C R = 10 s$

Substituting this value of $τ_{c}$ in Eq. (i) and solving for $t$ , we get

$t = 13.86 s$

$∴$ Correct answer is (a).

Electrostatics 6 Question 3

3. A $4 μ F$ capacitor and a resistance of $2.5 M Ω$ are in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, $\ln (2) = 0.693$ ]

Answer:

Solution:

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Electrostatics 6 Question 3

3. A 4μF capacitor and a resistance of 2.5MΩ are in series with 12 V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, ln⁡(2)=0.693 ]

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. A $4 μ F$ capacitor and a resistance of $2.5 M Ω$ are in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, $\ln (2) = 0.693$ ]