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It is possible to extend the circuit infinitely in both directions as shown in the figure. Knowing r=1 a) Calculate RAB when both locks are open or when K1 is closed K2 are closed b) Calculate RAB when K1 is closed K2 is open c) Calculate RAB when both locks are closed

User Armenm
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Answer:

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In the circuit shown in Figure, initially K

1

is closed and K

2

is open. What are the charges on each capacitor. Then K

1

was opened and K

2

was closed (order is important), What will be the charge on each capacitor now? [C=1μF]

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Solution

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When K

2

is open and K

1

is closed the capacitors C

1

and C

2

will charge and potential develops across them i.e., V

1

and V

2

respectively which will be equal to the potential of battery 9V

∴V

1

+V

2

=9……..I

∵V=

C

q

=orVα

C

1

Or

V

2

V

1

=

C

1

C

2

V

2

V

1

=

6C

3C

3V

2

=6V

1

V

2

=2V

1

…II

From Eqns. I and II

V

1

+2V

1

=9

3V

1

=9

V

1

=3

Volt

V

2

=2×3Volt=6Volt

∴q

1

=C

1

V

1

=6C×3=18C[(from II C=1μF)

=18×1μF=18μc

q

2

=C

2

V

2

=3C×6

=3×1μF×6=18μC

So, charges on each capacitor i.e., q

1

=q

2

=18μc

When k

1

is open and k

2

is closed then charge q

2

will be distributed among

C

2

and C

3

. Let it be q

2

and q

3

∴q

2

=q

2

+q

3

As C

2

and C

3

are now in parallel combination so their potentials

remain same (V)

∴q

2

=C

2

V+C

3

V

18μC=3×1μFxV+3×1μF×V

18=6V

V=3Volt

So potential on C

2

and C

3

capacitors are 3 Volt each

q

2

=C

2

V−3×1μF×3Volt=9μC

q

3

=C

3

V=3×1μF×3Volt=9μC

User Kbirk
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9.0k points