True False The resistance of wire B is twice as large as the resistance of wire

Question

True False  The resistance of wire B is twice as large as the resistance of wire A.
True False  The curent through the battery is five times larger than the current through wire B.
True False  The resistance of wire B is four times as large as the resistance of wire A.
True False  The voltage drop across wire B is larger than the voltage drop across wire A.
True False  The power dissipated in wire A is 16 times the power dissipated in wire B.

The picture shows a battery connected to two wires in parallel. Both wires are made of the same material and are of the same length, but the diameter of wire A is twice the diameter of wire B.

Explanation / Answer

Resistance (R) = rho * L/A = 4 rho * L/d^2
d = diameter, L = length of wire
--------------------------------------
length = same
diameter> dA = 2 dB
so>
R(A) = R(B)/4
R(B) = 4 R(A)
--------------------------------------

1) false > four times

2) box resistance of combination (Ro)
Ro = R(A) R(B)/[R(A) + R(B)] = 4 R(A)*R(A)/5 R(A)
Ro = [4/5] R(A)
I = current through battery = V/[4/5]R(A) = 5V/4R(A) --------- (1)
I(B) = current through B = V/R(B) = V/4 R(A) ------------ (2)
divide
I / I(B) = 5
(2) is true>>>>>

3) True > proved above

4)false> in parallel combination whatever be resistances in branches, voltage drop across each branch is SAME

5) Power = P(A) = V^2/R(A) >>>>>> at constant voltage
P(B) = V^2/R(B)
divide>
P(A)/P(B) = R(B)/R(A) = 4
its not 16 times, but 4 times
false

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