Exams › JEE Advanced › Physics

In a series L-R circuit connected to a battery of constant emf E, the switch is closed at t = 0. Let e be the magnitude of the emf induced across the inductor and i the circuit current at time t. Which graph correctly represents e versus i?

1. A straight line of e decreasing linearly with i, from a positive intercept down to zero
2. A curve where e decreases nonlinearly and approaches zero asymptotically
3. A curve where e increases nonlinearly from the origin and saturates
4. A straight line of e increasing linearly with i from the origin

Correct answer: A straight line of e decreasing linearly with i, from a positive intercept down to zero

Solution

By KVL around the L-R loop, E = i*R + L*di/dt, and the inductor emf magnitude is e = L*di/dt = E - i*R. This is linear in i: at t = 0, i = 0 so e = E (maximum); as i grows to its steady value E/R, e falls to 0. So the e-vs-i graph is a straight line decreasing from intercept E to zero.

Related JEE Advanced Physics questions

• What is the final velocity attained by the loop?
• A long coaxial cable is made up of two cylindrical conductors with radii a and b. The inner conductor carries a constant current i, while the outer conductor acts as the return path for the current. What is the self-inductance of a segment of the cable of length l?
• Determine the inductance per unit length for a loop created by connecting the ends of two infinitely long parallel wires, each with radius r, and separated by a distance d between their centers. Ignore the magnetic flux inside the wires and the effects at the ends.
• If the electromotive force is 10 V and the rate of change of current is calculated as 2.5 A/s, what is the self-inductance of the coil, given by L = e / (dl/dt)?
• The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
• A semicircular loop of radius r is positioned on the axis of a large current-carrying circular ring of radius R (with R >> r). The loop is placed at an axial distance of R*sqrt(3) from the center of the ring, and the plane of the semicircular loop makes an angle of 53 deg with the plane of the ring. Find the mutual inductance M between the two coils.

⚔️ Practice JEE Advanced Physics free + battle 1v1 →