Physics And Measurement Question 254

Question: A quantity X is given by $ {\varepsilon _{0}}L\frac{\Delta V}{\Delta t} $ where $ {\in _{0}} $ is the permittivity of the free space, L is a length, $ \Delta V $ is a potential difference and $ \Delta t $ is a time interval. The dimensional formula for X is the same as that of

Options:

A) Resistance

B) charge

C) Voltage

D) current

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Dimensionally $ {\varepsilon _{0}}L=C $ where C= capacitance Now the given expression reduces to $ C\Delta V/\Delta t. $ Dimensionally $ C\Delta V=q $ where q is charge. Again the given expression reduces to $ q/\Delta t. $ Dimensionally $ \frac{q}{\Delta t}=I $ where I is current



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