Match the dimensional formulas (in M-L-T-I notation) to quantities: (A) Resistance, (B) Inductance, (C) Capacitance, (D) Reluctance — with: (1) M^-1 L^-2 T^2 I^2, (2) M L^2 T^-2 I^-2, (3) M^-1 L^-2 T^4 I^2, (4) M L^2 T^-3 I^-2.

Introduction / Context:Dimensional analysis in electromagnetism relates electrical quantities to base dimensions M (mass), L (length), T (time), and I (current). Matching correct dimensions helps validate formulas and perform unit checks across problems.

Given Data / Assumptions:

• A: Resistance (ohm = V/A).
• B: Inductance (henry = V*s/A).
• C: Capacitance (farad = C/V).
• D: Reluctance (magnetic) is analogous to 1/inductance in dimensional terms.

Concept / Approach:Use base relations: V = W/Q = (J/s)/A = (M L^2 T^-3)/I; then compute each quantity by substitution and simplification.

Step-by-Step Solution:

Verification / Alternative check:Cross-check using energy in inductor W = (1/2) L I^2 → L = 2W / I^2; since W has dimensions M L^2 T^-2, L → M L^2 T^-2 I^-2, consistent with above.

Why Other Options Are Wrong:

• A-1, B-2, C-3, D-4: Assigns reluctance and resistance incorrectly.
• A-2, B-1, C-3, D-4: Misplaces resistance and inductance; reluctance not 4.
• A-2, B-4, C-3, D-1: Gives an impossible dimension (4) to inductance.

Common Pitfalls:

• Forgetting that resistance involves T^-3 (from V) rather than T^-2.
• Confusing magnetic reluctance with electrical resistance; they are analogous but dimensionally inverse to inductance.

Final Answer:A-4, B-2, C-3, D-1