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**Introductory Exercise 22.1**

**Ques 1: Find the dimensions of capacitance.****Sol: **

= [M^{-1}L^{-2}T^{4}A^{2}]**Ques 2: No charge will flow when two conductors having the same charge are connected to each other. Is this statement true or false?Sol:** Charge does not flow if their potentials are same.

Sol:

Hence, charges are as shown below

Sol:

Hence charge on different faces are as shown below.

Electric field and hence potential difference between the two plates is due to Â±2.5 q

**Introductory Exercise 22.2**

**Ques 1: Find the charge stored in all the capacitors.Sol:** All three capacitors are in parallel wit h the battery. PD across each of them is 10V. So, apply q = CV for all of them.

Sol:

Sol:

Now, potential difference across capacitor = potential difference across 4Î© resistance.

= iR

= (3)(4)=12V

q = CV = (2Î¼F) (12 V)

= 24Î¼C

(a) Find the charge on each capacitor and the voltage across them.

(b) The charged capacitors are disconnected from the line and from each other and reconnected with terminals of like sign together. Find the final charge on each and the voltage across them.

= 800Î¼C

In series, q remains same

q

and

(b) Now total charge will become 1600 Î¼C. This will now distribute in direct ratio of capacity

They will have a common potential (in parallel) given by.

Sol:

In parallel common potential is given by

Solving this equation we get

C = 400Î¼F

**Introductory Exercise 22.3**

**Ques 1: An uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.Sol: **Charge supplied by the battery,

q= CV

Energy supplied by the battery,

E = qV =CV

Energy stored in the capacitor,

âˆ´ Energy dissipated across R in the form of heat = E - U

Sol:

Sol:

q

While q

Now charge on capacitor changes from q

i = E/R

(b) Long after switch is closed no current will pass through C

(a) the initial current through each resistor

(b) steady state current through each resistor

(c) final energy stored in the capacitor

(d) time constant of the circuit when switch is opened.

Sol:

(b) In steady state no current flow through capacitor wire. PD across R

(c) In steady state potential difference across capacitor is E.

âˆ´

(d) When switch is opened, capacitor is discharged through resistors R

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