Test: Stokes Theorem - Electrical Engineering (EE) MCQ

Answer: d
Explanation: The curl of y i + z j + x k is i(0-1) – j(1-0) + k(0-1) =
-i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said to be irrotational.

Answer: c
Explanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.

Answer: d
Explanation: The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems convert line to surface integral.

Answer: Since curl is required, we need not bother about divergence property. The curl of the function will be i(0-0) – j(0-0) + k(0-0) = 0. The curl is zero, thus the function is said to be irrotational or curl free.

Answer: a
Explanation: It states that the line integral of a function gives the surface area of the function enclosed by the given region. This is computed using the double integral of the curl of the function.

Answer: d
Explanation: From Stoke’s theorem, we can calculate energy stored in an inductor as 0.5Li². E = 0.5 X 2 X 4² = 16 units.

Answer: a
Explanation: We can compute the energy stored in a capacitor from Stoke’s theorem as 0.5Cv². Thus given energy is 0.5 X 12 X v². We get v = 0.57 volts.

Answer: b
Explanation: From Stoke’s theorem, we can calculate P = E X I = ∫ E. J ds
= 2∫ x² dx as x = 0->1. We get P = 2/3 units.

Answer: d
Explanation: The current density is given by, J = σE. To find conductivity, σ = J/E = 1/200 X 10^-6 = 5000.

Answer: c
Explanation: Resistance calculated from Ohm’s law and Stoke’s theorem will be R = ρL/A. To get resistivity, ρ = RA/L = 200 X 20/10 = 400.