Units and Measurements · Question 4

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, the electrical conductivity and the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity Z= S2 is:

1. [M0L0T0I0K0]
2. [M0L0T0I0K-1]
3. [M1L2T-2I-1K-1]
4. [M1L2T-4I-1K-1]

Answer

(2) [M0L0T0I0K-1]

Solution

Write each quantity in base dimensions.

[S]= [V][K]=[ML2T-3I-1K-1], so [S2]=[M2L4T-6I-2K-2]

[ ]= 1[ ]=[M-1L-3T3I2]

[ ]= [power][L][K]=[MLT-3K-1]

[Z]= [M2L4T-6I-2K-2][M-1L-3T3I2][MLT-3K-1]=[M0L0T0I0K-1]

Answer: (B)