a wire of 15 ohm resistance is gradually stretched to double its original length. it is then cut into two equal parts. these parts are connected in parallel across a 3 V cell. find the current drawn from the cell

Let R0, l0, A0 be the original resistance, length and area of the wire.

Let R, l, A be the original resistance, length and area of the stretched wire. Since the length is doubled ; l =2l0

When the wire is stretched its Volume remains the same.

Therefore, V= Al = A0l0

    A(2l0) = A0l0

    A=A0/2

Resistance R=ρl/A

R/R0 = lA0/l0A

R/R0 = 2l0 A0/ (l0 (A0/2)) = 4

R = 4R0 = 4x15 = 60Ω

 When the resistance of wire R=60Ω is cut into two equal parts, the length becomes half but area remains the same. Hence resistance of each part is R­1= R/2 = 60/2 = 30Ω

 

When these two wires of resistance 30Ω are connected in parallel across a 3V battery, the equivalent resistance Rp = R1/2 = 30/2 =15 Ω

(1/Rp = (1/ 30) +( 1/ 30) = 2/30 = 1/15

Rp =15Ω )

Therefore the current through the circuit is V/Rp = 3/15 = 0.2A

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current drawn = 0.1 A.

Soln. As l is doubled, Resistance increases to 8 times. = 120

When we cut it, both resistance= 60 ohm...

If we connect them in parallel , resistance = by parallel formula = 30 ohm

current = voltage/resistance = 3/30 = 0.1 A

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 Let R0, l0, A0 be the original resistance, length and area of the wire.
Let R, l, A be the original resistance, length and area of the stretched wire. Since the length is doubled ; l =2l0
When the wire is stretched its Volume remains the same.
Therefore, V= Al = A0l0
    A(2l0) = A0l0
    A=A0/2
Resistance R=ρl/A
R/R0 = lA0/l0A
R/R0 = 2l0 A0/ (l0 (A0/2)) = 4
R = 4R0 = 4x15 = 60Ω
 When the resistance of wire R=60Ω is cut into two equal parts, the length becomes half but area remains the same. Hence resistance of each part is R­1= R/2 = 60/2 = 30Ω
 
When these two wires of resistance 30Ω are connected in parallel across a 3V battery, the equivalent resistance Rp = R1/2 = 30/2 =15 Ω
(1/Rp = (1/ 30) +( 1/ 30) = 2/30 = 1/15
Rp =15Ω )
 
Therefore the current through the circuit is V/Rp = 3/15 = 0.2A 
 
 
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Answer

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