Dimensional analysis – Match circuit quantities to their dimensional formulas List I (Quantity) A. Resistance B. Inductance C. Capacitance List II (Dimensions in M–L–T–I form) M^-1 L^-2 T^4 I^2 M L^2 T^-2 I^-2 M L^2 T^-3 I^2 ← (note: commonly written with I^-2 for resistance) Choose the correct mapping.

Introduction / Context:
Engineering quantities can be expressed via base dimensions Mass (M), Length (L), Time (T), and Current (I). Remembering these helps verify formulas and catch unit mistakes in circuit analysis and electromagnetics.

Given Data / Assumptions:

• Ohm (resistance) = Volt/Ampere.
• Henry (inductance) = Volt·second/Ampere.
• Farad (capacitance) = Coulomb/Volt.
• Standard base: V = M L^2 T^-3 I^-1, A = I, Q = I·T.

Concept / Approach:

Compute dimensional forms from definitions: R = V/A, L = (V·s)/A, C = Q/V. Substitute base dimensions and simplify exponents carefully, paying attention to powers of I (current) because sign errors there are common in printed tables.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with any EM/circuits handbook: R → M L^2 T^-3 I^-2, L → M L^2 T^-2 I^-2, C → M^-1 L^-2 T^4 I^2. Minor typographic variances sometimes flip the sign on I; the physical relation clarifies the correct exponents.

Why Other Options Are Wrong:

Options that swap R with C or L contradict the base-unit derivations above; particularly, resistance cannot have the same T power as inductance.

Common Pitfalls:

Forgetting that V scales as M L^2 T^-3 I^-1; mishandling current powers when dividing by A (I), which should decrease the exponent by one.

Final Answer:

A-3, B-2, C-1.