two metallic wires And and B are connected in second wire A has length l and radius r while wire B has length 2l and radius 2r . Find the ratio of total resistance of series combination and the resistance of wire A, if both the wires of same material?
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Suppose the resistivity of both the wires is ‘q’.
Resistance of wire A is, Ra = ql/(πr2)
Resistance of wire B is, Rb = q(2l)/[π(2r)2] = ql/(2πr2)
Now, the resistance when they are connected in series is, R = Ra + Rb = (3/2)[ql/(πr2)]
So, the required ratio is, R : Ra = (3/2)[ql/(πr2)] : ql/(πr2)
=> R : Ra = 3 : 2
Resistance of wire A is, Ra = ql/(πr2)
Resistance of wire B is, Rb = q(2l)/[π(2r)2] = ql/(2πr2)
Now, the resistance when they are connected in series is, R = Ra + Rb = (3/2)[ql/(πr2)]
So, the required ratio is, R : Ra = (3/2)[ql/(πr2)] : ql/(πr2)
=> R : Ra = 3 : 2
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