Find the dimension formula for inductance and also the dimension formula for resistance.

The dimension formulas for inductance and resistance are derived from their definitions and the fundamental units of measurement in physics.

Inductance

Inductance (L) is a measure of how much voltage is induced in a circuit due to a change in current. The formula for inductance is:

L = V / (dI/dt), where V is voltage, dI is the change in current, and dt is the change in time.

Using the dimensions of voltage (V), current (I), and time (T), we can express inductance in terms of base units:

• Voltage (V) has the dimension of [M L² T⁻³ I⁻¹]
• Current (I) has the dimension of [I]
• Time (T) has the dimension of [T]

Thus, the dimension formula for inductance is:

[M L² T⁻² I⁻²]

Resistance

Resistance (R) quantifies how much a material opposes the flow of electric current. The formula for resistance is:

R = V / I, where V is voltage and I is current.

Using the same dimensions as before, we can express resistance as follows:

• Voltage (V): [M L² T⁻³ I⁻¹]
• Current (I): [I]

Therefore, the dimension formula for resistance is:

[M L² T⁻³ I⁻²]