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Find the dimensions of the quantity L / (R C V), where L is inductance, R is resistance, C is capacitance and V is potential difference. (Symbols carry their usual meaning.)

1. [A⁻¹] (reciprocal of current, i.e. ampere⁻¹)
2. [A] (current)
3. [M L² T⁻³ A⁻¹] (volt)
4. dimensionless

Correct answer: [A⁻¹] (reciprocal of current, i.e. ampere⁻¹)

Solution

L/R is the time constant, with dimension [T]. C V = Q, the charge, with dimension [A T]. Thus L/(RCV) = [T]/[A T] = [A⁻¹], the reciprocal of current.

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