1. [1pt] The picture shows a battery connected to two cylindrical resistors in p

Question

1. [1pt]
The picture shows a battery connected to two cylindrical resistors in parallel. Both resistors are made of the same material and are of the same length, but the diameter of resistor A is twice the diameter of resistor B.
(For each statement select T True, F False).

A) The current through wire A is four times larger than the current through wire B.
B) The current through the battery is five times larger than the current through wire B.
C) The power dissipated in resistor A is 16 times the power dissipated in resistor B.
D) The resistance of resistor B is four times larger than the resistance of resistor A.
E) The voltage drop across resistor B is the same as the voltage drop across resistor A.

Explanation / Answer

here,

Resistance R = rho L/A

R1 = rho L/(pi r1^2)

R2 = rho L/(pi r2^2)

here r1 = D/2

r2 = 2D/2 = D = 2 r1

ohms V = iR

so

part A: Ia Ra = Ib Rb

Ia/Ib = Rb/Ra = 4 r1^2/r1^2 = 4

ia is four times so A is True

Part B is Flase

part C:

Powe P = i^2/R

Pb/Pa = (ib/ia)^2 * Ra/Rb

Pb/Pa = 1/16

so Part C is true

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part E: true

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