SATHEE: Electrostatics 7 Question 17

Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

(2016 Adv.)

(a) proportional to $V_{0}^{2}$ .

(b) proportional to the potential $V_{0}$ .

(d) proportions to $V_{0}^{1 / 2}$

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Answer:

Correct Answer: 17. (a)

Solution:

As the balls keep on carrying charge form one plate to another, current will keep on flowing even in steady state. When at bottom plate, if all balls attain charge $q$ ,

$\begin{aligned} \frac{k q}{r} & = V_{0} & ∴ k = \frac{1}{4 π ε_{0}} \\ \Rightarrow & q & = \frac{V_{0} r}{k} \end{aligned}$

Inside cylinder, electric field $E = [V_{0} - (- V_{0})] h$

$= 2 V_{0} h$

$\Rightarrow$ Acceleration of each ball,

$a = \frac{q E}{m} = \frac{2 h r}{k m} \cdot V_{0}^{2}$

$\Rightarrow$ Time taken by balls to reach other plate,

$t = \sqrt{\frac{2 h}{a}} = \sqrt{\frac{2 h \cdot k m}{2 h r V_{0}^{2}}} = \frac{1}{V_{0}} \sqrt{\frac{k m}{r}}$

If there are $n$ balls, then

Average current, $i_{a v} = \frac{n q}{t} = n \times \frac{V_{0} r}{k} \times V_{0} \sqrt{\frac{r}{k m}}$

$\Rightarrow i_{a v} \propto V_{0}^{2}$

Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

Answer:

Solution:

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Electrostatics 7 Question 17

17. The average current in the steady state registered by the ammeter in the circuit will be

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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