What is the Dimensional Formula of Electrical Resistance?

To find the dimension of Resistance, we must start with the most fundamental equation in electricity: Ohm's Law. Ohm's Law states: V = I × R (Voltage = Current × Resistance).

Step 1: Rearrange the formula to isolate Resistance (R): R = V / I

Step 2: We need the dimensions for Voltage (V) and Current (I).

• Current (I) is a fundamental base quantity. Its dimension is simply [A] (Ampere).
• Voltage (V) is derived as Work Done / Charge (W/Q).
  • Work Done (W) = Force × Distance = [M¹ L² T⁻²]
  • Charge (Q) = Current × Time = [A¹ T¹]
  • Therefore, Dimension of Voltage (V) = [M¹ L² T⁻²] / [A¹ T¹] = [M¹ L² T⁻³ A⁻¹]

Step 3: Now, plug the dimension of Voltage back into our original Ohm's Law equation (R = V / I).

• R = [M¹ L² T⁻³ A⁻¹] / [A¹]
• When you bring the [A¹] from the denominator to the numerator, it becomes [A⁻¹].
• A⁻¹ × A⁻¹ = A⁻²

Final Dimension of Resistance (R) = [M¹ L² T⁻³ A⁻²].

While the dimensional formula looks highly complex, the official SI unit of Resistance is simply called the Ohm (Ω), named after the German physicist Georg Simon Ohm who discovered the relationship between current and voltage.