Half-wave controlled rectifier with RL load and freewheeling diode A single-phase half-wave controlled rectifier supplies an RL load and includes a freewheeling diode. The input is v(t) = Vm sin(ωt). If I0 is the load current during the freewheeling interval, what is the KVL governing equation while the freewheeling diode conducts?

Introduction / Context:
Freewheeling diodes in controlled rectifiers provide a path for inductive current when the source voltage becomes unfavorable, preventing abrupt current interruption and large overvoltages. Writing the correct KVL during the freewheel interval is fundamental for analyzing current decay and ripple.

Given Data / Assumptions:

• Single-phase half-wave controlled rectifier feeding RL.
• Freewheeling diode across the load.
• During freewheeling, source is effectively isolated from the load loop.

Concept / Approach:

When the freewheeling diode conducts, the loop consists only of R, L, and the diode (assumed ideal with negligible drop). Therefore the source does not appear in the loop equation; current decays according to a homogeneous first-order differential equation.

Step-by-Step Solution:

Verification / Alternative check:

Solution i(t) = I0 * exp(−t/τ) with τ = L/R confirms exponential decay independent of source voltage during freewheel.

Why Other Options Are Wrong:

Options that include Vm sin(ωt) presume the source is in the loop; not true during freewheeling. Signs in (e) are incorrect for passive sign convention.

Common Pitfalls:

Forgetting to remove the source from the loop during the freewheel interval; neglecting diode drop is acceptable for first-order analysis.

Final Answer:

L * (di/dt) + R * i = 0