Question

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

​

Answer 1

ʜᴏᴘᴇ ɪᴛ's ʜᴇʟᴘғᴜʟ

Explanation:

Hence, dimensional formula for inductance is [L]=[AT−1ML2T−3A−1]=[ML2T−2A−2

Answer 2

Answer:

Dimensional formula of ;

1. Resistance is M L² T-³ I-²
2. Inductance is MT−²L²A−²

Explanation:

Dimensional formula for Resistance ;

The dimensional formula of resistance is given by,

→M¹L² T-² I-²

Where,

→ M = Mass

→ I = Current

→ L = Length

→ T = Time

→Resistance (R) = Voltage × Current-¹ ————–(i)

→Since, voltage (V) = Electric Field × Distance

= [Force × Charge-¹] × Distance

→The dimensional formula of charge = current × time = I¹ T¹

→The dimensional formula of voltage = [Force × Charge-¹] × Distance

= [M¹ L¹ T-²] × [I¹ T¹]-¹× [L¹] = [M¹L² T-³ I-¹] ———–(ii)

On substituting equation (ii) in equation (i) we get,

→Resistance (R) = Voltage × Current-1

→R = [M¹ L² T-³ I-¹] × [I]-¹ = [M¹ L² T-³ I-²]

Therefore, resistance is dimensionally represented as M L² T-³I-².

________________

Dimensional formula for Inductance ;

For inductance, the defining equation is,

→ϕ=LI

→ But ϕ has units [(magnetic field)*(length)]²

→Magnetic field from Lorentz force law has units,

→ (Force)(velocity)-¹(charge) -¹

Therefore, dimensions of magnetic field,

→[B]=MLT−² / LT−¹AT

→[B]=MLT−² / LA

→[B]=MT−²A−¹

Therefore dimensions of magnetic flux,

→[ϕ]=[B]L²

→[ϕ]=MT−²L²A−¹

Hence, the dimensions of inductance,

→[L]=[ϕ][I][L]=MT−²L²A−²

Therefore, inductance is dimensionally represented as MT−²L²A−².