Question

The disadvantage of Hopkinson's test on two dc shunt machines is

• A. \( \text{copper and iron losses are assumed equal} \)
• B. \( \text{requires two unidentical machines} \)
• C. \( \text{iron and mechanical losses are assumed equal} \)
• D. \( \text{iron and mechanical losses are assumed unequal} \)

Hint:

Hopkinson's test requires two identical machines, which rules out option (2). Its main drawback lies in assuming that the stray losses (iron + mechanical losses) can be cleanly halved and shared equally between the motor and generator, ignoring the differences in field excitation.

Answer 1

The Correct Option is C

Concept: Hopkinson's test, also widely referred to as the regenerative test or back-to-back test, is a full-load test performed to determine the efficiency of DC machines without wasting a large amount of power. The test requires two mechanically coupled identical DC shunt machines. One machine operates as a motor, driving the second machine, which acts as a generator. The electrical output of the generator is fed back into the electrical input of the motor. The total power drawn from the external supply grid only accounts for the total internal losses of both machines combined. While highly advantageous for full-load temperature testing, it relies on certain simplifying assumptions during calculation.

Step 1: Identify the main assumption in stray loss calculations.
During the test analysis, the combined stray losses (which include core/iron losses and mechanical friction/windage losses) are calculated for the two machines together from the net input power from the supply. Let $P_{\text{stray, total}}$ be this measured value. The standard assumption made to simplify calculation is that these stray losses are distributed equally between the two coupled machines: $$P_{\text{stray, motor}} = P_{\text{stray, generator}} = \frac{P_{\text{stray, total}}}{2}$$

Step 2: Understand why this assumption is a disadvantage.
In reality, the iron loss depends on the core flux ($\phi$). Because the motor field current is adjusted differently from the generator field current to enable power flow between them, their operating fluxes are not identical: $$\phi_{\text{motor}} \neq \phi_{\text{generator}}$$ Consequently, the actual iron losses are unequal. Furthermore, mechanical friction and windage losses depend on speed, which is identical, but assuming iron and mechanical components can be split symmetrically or that their inner individual proportions are equal introduces small errors in the precise efficiency computation of each separate unit. Specifically, the test assumes that the combined stray losses (iron and mechanical components) are identical for both units under comparison.

Step 3: Evaluate the options.
Reviewing option (3), it highlights that "iron and mechanical losses are assumed equal" across the two machines as the primary calculated baseline constraint. This is an oversimplification and represents a disadvantage of the test. Thus, option (3) is correct.