Two spherical conductors of capacitance 3.0mF and 5.0mF are charged to potentials of 300volt and 500volt. The two are connected resulting in redistribution of charges. Then the final potential isa)300 voltb)500 voltc)425 voltd)400 voltCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Solution:

Given, capacitance of first conductor, C1 = 3.0mF
Capacitance of second conductor, C2 = 5.0mF
Potential of first conductor, V1 = 300V
Potential of second conductor, V2 = 500V

When the two conductors are connected, the charges will redistribute until they reach a common potential.

Let the final potential be V.

Charge on the first conductor, Q1 = C1V1 = 3.0mF x 300V = 900mC
Charge on the second conductor, Q2 = C2V2 = 5.0mF x 500V = 2500mC

Total charge before connection, Q = Q1 + Q2 = 900mC + 2500mC = 3400mC

Total capacitance after connection,
1/C = 1/C1 + 1/C2 = (C1 + C2) / (C1C2) = 8 / 15mF
C = 15/8mF

Using the formula, Q = CV
V = Q/C = (3400 x 10^-6) / (15/8 x 10^-3) = 680V

Therefore, the final potential is 680V.

But this is not one of the options given in the question.

To find the correct answer, we need to use the principle of conservation of charge.

The total charge after connection should be the same as the total charge before connection.

Let Qf be the charge on the first conductor after redistribution.
Then, the charge on the second conductor after redistribution is Q - Qf.

Using the formula for capacitance, Q = CV, we can write:
Qf = C1V and Q - Qf = C2V

Substituting the given values, we get:
Qf = 3.0mF x V and Q - Qf = 5.0mF x V

Adding these two equations, we get:
Q = 8.0mF x V

Substituting the total charge, Q = 3400mC, we get:
3400mC = 8.0mF x V
V = 425V

Therefore, the final potential is 425V, which is option (c).

Answer

First find the charge in 1st capacitor
Q1= C1*V1
=0.003*300
=0.9 C
Similarly, find Q2
i.e. Q2=2.5 C
After connecting the capacitors in parallel you get a net capacitance C=8 mF (c1+c2).

Thus, final potential is V=Q/C
Q=Q1+Q2=3.4 C

V=3.4/0.008
= 425 V

Hope you understood. Thank you

Answer

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