Question

Two wires P and Q of same material are connected in series as shown in figure. Cross-sectional area and length of wire P are A and L respectively. Wire Q having area half of area of P and length double of length P. Total resistance of given arrangement is -
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Answer 1

Given:

Cross sectional area of wire P = A

Length of wire P = l

Cross sectional are of wire Q = A/2

Length of wire Q = 2l

To find:

Total resistance of the given arrangement.

Solution:

As we know that, Req = R1 + R2 (in series)

Where Resistance R = ρl/ A

Since the material of both the wires are same hence ρ will be same for both the wires.

Resistance of wire P = ρl / A

Resistance of wire Q = ρ*2l/ (A/2) = 4ρl / A

Equivalent resistance (Req) = ρl/A + 4ρl/A

= 5ρl /A

Therefore the total resistance will be 5ρl/A.