Sat June 18, 2011 By: Gurleen Kaur

Two metallic wires A and B of same material are connectedin parallel. Wire A has length l and radius r and wire B has length 2l. Compute the ratio of the total resistance of parallel combination and the resistance of wire A?

Expert Reply
Sun June 19, 2011

The electrical resistance of a uniform conductor is given in terms of resistivity by:

where l is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = ?r2 if r is radius) in units of meters squared, and ? is the resistivity in units of ohm·meters.

Resistance in parallel will be
Now the ratio between total resistance and reistance of wire A is
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