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Question

Choose the correct dimensional formula of 5CV.
(C is capacitance and V is potential difference)

A
[ML2T3A2]
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B
[M1L0T1A1]
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C
[MLT2A1]
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D
[MLT1A1]
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Solution

The correct option is D [MLT1A1]
We have the well known equation

Q=CV

And the number 5 is dimensionless. So, the expression has the same dimensional formula as that of charge.

Electric current is the rate of flow of charge.

I=QtQ=It

The physical quantities current and time are both fundamental units in the SI system.

Therefore, dimensional formula of charge Q will be [A1T1] or you can say [M0L0T1A1].

Hence, option (c) is correct.
Key Concept: The relation between charge, potential difference, and capacitance of a capacitor is Q=CV.

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