Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET
Exam
NEET
Subject
Physics
Chapter
Electromagnetic Induction

NEET · Physics · Electromagnetic Induction

A branch of an electrical circuit between points M and N contains...

A branch of an electrical circuit between points M and N contains an ideal inductor of 1 H1 \text{ H}, a battery of 3 V3 \text{ V}, and a resistor of 2 Ω2 \ \Omega connected in series. The current flows from M to N. The negative terminal of the battery is connected towards M and the positive terminal towards N. The current ii (in A) varies with time tt (in s) as a straight line passing through the coordinates (t=0,i=1)(t=0, i=1) and (t=2,i=5)(t=2, i=5) on an i−ti-t graph. What is the potential difference VM−VNV_M - V_N at t=1 st = 1 \text{ s}?

Options

  1. A6 V6 \text{ V}
  2. B3 V3 \text{ V}
  3. C11 V11 \text{ V}
  4. D5 V5 \text{ V}

Correct answer

D. 5 V5 \text{ V}

Step-by-step solution

From the given coordinates (0,1)(0, 1) and (2,5)(2, 5), the rate of change of current is the slope of the i−ti-t graph:
didt=5−12−0=2 A/s\dfrac{di}{dt} = \dfrac{5 - 1}{2 - 0} = 2 \text{ A/s}

The current at t=1 st = 1 \text{ s} can be found from the linear relation i=1+2ti = 1 + 2t:
i=1+2(1)=3 Ai = 1 + 2(1) = 3 \text{ A}

Applying Kirchhoff's Voltage Law from M to N:
VM−Ldidt+E−iR=VNV_M - L\dfrac{di}{dt} + E - iR = V_N
Note that the battery is traversed from the negative to the positive terminal, so its potential change is +3 V+3 \text{ V}.

Substituting the values:
VM−(1)(2)+3−(3)(2)=VNV_M - (1)(2) + 3 - (3)(2) = V_N
VM−2+3−6=VNV_M - 2 + 3 - 6 = V_N
VM−5=VNV_M - 5 = V_N
VM−VN=5 VV_M - V_N = 5 \text{ V}

Answer: 5 V5 \text{ V}
Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

A square loop of area A is moving out of the uniform magnetic field (B) with constant… MHT CET Medical 2026The value of mutual inductance of two coils is 6 mH. The current in one of the coil… MHT CET Medical 2026Two identical inductors are connected in parallel. If the parallel combination stores 40\… MHT CET Medical 2026Two coils have mutual inductance of 0.004\ H . The current changes in the first coil… MHT CET Medical 2026The coefficient of coupling is 0.8 . If the mutual inductance is 8\ H , then the values… MHT CET Medical 2026The self inductance L of a solenoid of length l and area of cross-section A, with a fixed… MHT CET Medical 2026A wire of length 1\ m is moving at a speed of 2\ m/s perpendicular to its length in a… MHT CET Medical 2026Semicircular wire of radius R is rotated in a uniform magnetic field about an axis… MHT CET Medical 2026 Full Electromagnetic Induction list All NEET PYQs