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Question

Find the dimension formula for resistance.


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Solution

Step 1: Establish Resistance in terms of Standard Quantities

The formula for Resistance according to Ohm's law is given as,

R=VI

Where, V is the potential difference, and I is the electric current.

The formula for potential difference is,

V=EL

Where, E is the electric field, L is the length between the two points in a conductor.

The formula for electric field is,

E=Fq

Where, F is force, and q is electric charge.

∴E=maqwhere m is the mass and a is the acceleration.

∴V=maLq

∴R=maLqI

Step 2: Evaluate the Dimensional Formula

Substitute the standard units into the above equation to get,

L=kg.ms-2.mAs.A

=kg.m2.s-3.A-2

=ML2T-3A-2

Hence the dimensional formula for inductance is ML2T-3A-2.


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