When the damping force is more than the optimum, the instrument will become

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Slow and lethargic

Explanation: When the damping force exceeds the optimum (critical) damping level, the instrument becomes overdamped. This causes the pointer to approach its steady-state position very slowly, resulting in a lethargic and sluggish response.

Working Principle: An instrument's response is governed by the second-order differential equation $J \frac{d^2	heta}{dt^2} + D \frac{d	heta}{dt} + K	heta = T_d$. When $D > D_c$ (where $D_c = 2\sqrt{KJ}$ is the critical damping coefficient), the system is overdamped. The roots of the characteristic equation are real and negative, preventing oscillation but significantly increasing the time required for the pointer to settle.

Key Formulas: $D_c = 2\sqrt{KJ}$ — critical damping coefficient; $\zeta = \frac{D}{2\sqrt{KJ}}$ — damping ratio

Key Points: Critical damping ($\zeta = 1$) is usually desired for the fastest response without oscillation.; Overdamping ($\zeta > 1$) leads to a sluggish response.; Underdamping ($\zeta; Damping torque is generated by eddy currents, fluid friction, or air friction.

Advantages: Prevents oscillations around the equilibrium position.; Protects the pointer mechanism from erratic swings.

Disadvantages: Excessive damping increases measurement time significantly.; May lead to reading errors due to slow response to signal changes.

Applications: Moving coil instruments; Analog voltmeters and ammeters

Additional Info: The 'optimum' state is defined as being slightly underdamped or critically damped for a balance of speed and overshoot.. Option B (Oscillating) corresponds to an underdamped state.. Option A (Dead) is a misnomer, as a dead instrument typically implies no movement at all (e.g., open circuit).

Answer: C is correct — When damping is greater than critical, the instrument becomes overdamped, resulting in a slow and lethargic movement of the pointer.

Exam Tip: Always remember: Critically damped systems reach steady state the fastest without any overshoot, making them ideal for high-precision measurement.

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