Question

What are the dimensional formula units for voltage?

Hint:

Voltage has the dimensional formula \( M^1 L^2 T^{-3} A^{-1} \), which is derived from the relationship between energy and charge.

Answer 1

Step 1: Understanding voltage dimensions.
Voltage (or electric potential) is defined as energy per unit charge. The dimensional formula for energy is \( M L^2 T^{-2} \), and for charge, it is \( A T \). Dividing energy by charge gives the dimensional formula for voltage: \[ [V] = \frac{M L^2 T^{-2}}{A T} = M L^2 T^{-3} A^{-1} \]

Answer 2

Step 1: Voltage is energy divided by charge.

Step 2: Energy has the dimensional formula ML²T⁻², and charge has AT.

Step 3: Dividing energy's formula by charge's formula: ML²T⁻² ÷ AT = ML²T⁻³A⁻¹.

Step 4: So the dimensional formula of voltage is ML²T⁻³A⁻¹.

Answer 3

Step 1: Use the power-current relation instead of energy-charge. Electrical power is \( P = VI \), so \( V = \dfrac{P}{I} \).
Step 2: The dimensional formula of power is \( [P] = M L^2 T^{-3} \) (energy per unit time), and current has the base dimension \( [I] = A \).
Step 3: Dividing, \[ [V] = \frac{M L^2 T^{-3}}{A} = M L^2 T^{-3} A^{-1} \] which is the same result reached via energy per unit charge.