Electrical Resistance (R) is the opposition to the flow of electric current. To find its dimension, we must use Ohm's Law (V = IR) and break down Voltage (Potential) into fundamental units.
Formula: Resistance = Voltage / Current.
Dimensional Formula: [M L² T⁻³ A⁻²].
SI Unit: Ohm (Ω).
Dimension of Voltage (V): [M L² T⁻³ A⁻¹].
Step 1: Ohm's Law Resistance = Voltage / Current (R = V / I)
Step 2: Find Dimension of Voltage (V) Voltage (Potential) = Work Done / Charge (V = W / q)
Step 3: Find Dimension of Resistance Now, substitute Voltage back into Ohm's Law: R = Voltage / Current
Final Dimensional Formula: [M L² T⁻³ A⁻²]
The dimensional formula of electrical resistance is [M L² T⁻³ A⁻²].
Voltage is Work divided by Charge. Work is [M L² T⁻²] and Charge is [A T]. So Voltage is [M L² T⁻³ A⁻¹].
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