1-Two conductors of equal lengths are connected separately to identical batterie

Question

1-Two conductors of equal lengths are connected separately to identical batteries so that each has the same potential difference across it. The conductors are made of the same material but have different radii: the thicker conductor has twice the radius of the thinner conductor. Which of the two conductors dissipates a larger amount of power and by how much? Explain.

2-Suppose you have two capacitors and want to use them to store the maximum amount of energy by connecting them across a voltage source. How should you connect them? Support your answer with calculations.

Explanation / Answer

since Radius R2 = 2 R1

from resistance formula R = rho L/A

here length are same and materials are same

so

R1 = rhoL/pi r1^2

R2 = rho L/ pi ( 2r1)^2 = R1/4

Power Dissipated P = iR^2

so for V1, P1 = iR1^2

for V2, P2 = i (R1/4)^2 = 16 P1

so condcutor with smaller radii dissipated more power 16 times

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if C1 and C2 are the individual capacitor are connected in series,

then their resultant capaciatnce 1/Cnet = 1/C1+1/C2 or Cnet = C1C2/(C1+C2)

if c1 and C2 are connected in parallel, then their effective capacitancen is Cnet = C1+C2

also in sereis combination same amount of charge passes through each of the capacitiors

and in parallel combination, same PD (voltage) exists across each of the capacitor

Energyy U = 0.5CV^2

for U to be more , Cnet has to be more

Cnet will be more in parallel Combination

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