Study Guides/Physics/Dimensional Formula of Resistance
Study Guide · Physics

Dimensional Formula of Resistance (R)

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.

Question (Click to Flip)

What is the dimensional formula of resistance?

Answer

The dimensional formula of electrical resistance is [M L² T⁻³ A⁻²].

Card 1 of 2 free previews

Key Facts

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-by-Step Derivation

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)

  • Work Done = [M L² T⁻²]
  • Charge = Current × Time = [A T]
  • Voltage [V] = [M L² T⁻²] / [A T] = [M L² T⁻³ A⁻¹]

Step 3: Find Dimension of Resistance Now, substitute Voltage back into Ohm's Law: R = Voltage / Current

  • Current [I] = [A]
  • R = [M L² T⁻³ A⁻¹] / [A]
  • R = [M L² T⁻³ A⁻²]

Final Dimensional Formula: [M L² T⁻³ A⁻²]

SI Unit

  • SI Unit: Ohm (Ω).
  • From the formula V/I, 1 Ohm is equal to 1 Volt per Ampere (V/A).

Questions and Answers

What is the dimensional formula of resistance?+

The dimensional formula of electrical resistance is [M L² T⁻³ A⁻²].

How do you find the dimension of voltage?+

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].

More in Physics

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.