JEE Advanced2025PhysicsUnits and DimensionsActual
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= S^2 is :-
Options
- A[M^0 L^0 T^0 I^0 K^0 ]
- B[M^0 L^0 T^0 I^0 K⁻¹ ]
- C[M^1 L^2 T⁻² I⁻¹ K⁻¹ ]
- D[M^1 L^2 T⁻⁴ I⁻¹ K⁻¹ ]
Correct answer
B. [M^0 L^0 T^0 I^0 K⁻¹ ]
Step-by-step solution
aligned & S = emf per unit temperature difference & = Electrical conductivity & k = Thermal conductivity & [ S ]= [ ML ^2 ~T ⁻³ I ⁻¹ ~K ⁻¹ ] & [ ]= [ M ⁻¹ ~L ⁻³ ~T ^3 I ^2 ] & [ K ]= [ M ^1 ~L ^1 ~T ⁻³ ~K ⁻¹ ] & [ Z ]= S ^2 ~K = [ M ^1 ~L ^1 ~T ⁻³ ~K ⁻² ] [ M ^1 ~L ^1 ~T ⁻³ ~K ⁻¹ ] aligned [ Z ]= [ K ⁻¹ ]