Dynamometer wattmeter in an AC circuit: identify what quantity it indicates when connected correctly under sinusoidal steady state.

Introduction / Context:Dynamometer wattmeters are widely used for measuring power in alternating-current (AC) circuits. They utilize two coils (current coil and pressure/voltage coil) whose interaction produces torque proportional to the average value of the instantaneous power over a cycle. This question checks your understanding of what an electrodynamometer actually indicates.

Given Data / Assumptions:

• Proper connection of current coil in series and pressure coil across the load.
• Sinusoidal steady state; instrument constants are idealized.
• Scale is calibrated in watts.

Concept / Approach:

The instantaneous torque in a dynamometer wattmeter is proportional to v(t) * i(t). The pointer comes to rest when the average torque over a cycle is balanced by the control spring—hence the deflection is directly proportional to the average value of v(t) * i(t), which is real (true) power P = V_rms * I_rms * cosφ.

Step-by-Step Solution:

Verification / Alternative check:

If cosφ = 0 (purely reactive), average power is zero and the wattmeter shows nearly zero—matching real power behavior, not apparent or peak power.

Why Other Options Are Wrong:

• rms power / peak power / instantaneous power: not meaningful outputs for wattmeters; the instrument averages over a cycle.
• apparent power (VA): needs power factor; dynamometer alone does not indicate it.

Common Pitfalls:

• Confusing real power with apparent power.
• Assuming the pointer shows a snapshot (instantaneous) value; it does not.

Final Answer:

average power (real power)