In an electrostatic instrument, the sensitivity can be increased by ___________.

Question

Examoogle · Accepted Answer

The correct answer is Option C: increasing the area of the plates. The sensitivity of an electrostatic instrument is directly proportional to the rate of change of the deflecting torque with respect to the voltage. By increasing the area of the plates, the capacitance of the system is increased, which enhances the electrostatic force exerted between the plates for a given voltage, thereby increasing the instrument's sensitivity.

Step-by-Step Solution & Concepts:
The sensitivity of an electrostatic instrument is directly proportional to the rate of change of the deflecting torque with respect to the voltage. By increasing the area of the plates, the capacitance of the system is increased, which enhances the electrostatic force exerted between the plates for a given voltage, thereby increasing the instrument's sensitivity.

Working Principle: Electrostatic instruments operate on the principle of force of attraction between two charged surfaces. The deflecting torque $T_d$ is given by $T_d = \frac{1}{2} V^2 \frac{dC}{d	heta}$, where $C$ is the capacitance and $	heta$ is the angular deflection. Since $C = \frac{\epsilon A}{d}$, increasing the area $A$ directly increases $C$, and consequently, the rate of change of capacitance $\frac{dC}{d	heta}$ increases, resulting in a higher sensitivity.

Key Formulas: $C = \frac{\epsilon A}{d}$ — formula for capacitance where $A$ is the area of plates; $T_d = \frac{1}{2} V^2 \frac{dC}{d	heta}$ — deflecting torque for electrostatic instruments; $S = \frac{d	heta}{dV}$ — sensitivity as the change in deflection per unit voltage

Key Points: Electrostatic instruments are essentially voltmeters that respond to voltage rather than current.; They draw negligible current and are ideal for high-voltage measurements.; Sensitivity is enhanced by maximizing the change in capacitance relative to deflection.; Electrostatic force is extremely small, so these instruments require delicate moving parts.

Advantages: Negligible power consumption as they draw no continuous current.; Applicable for both AC and DC measurements.; Free from hysteresis and eddy current errors due to lack of permanent magnets.

Disadvantages: Non-linear scale due to the $V^2$ relationship.; High sensitivity to mechanical friction due to extremely low deflecting torque.; Large size required for high voltage isolation.

Applications: Measurement of very high voltages.; Used as laboratory standard voltmeters.

Additional Info: Option D is incorrect because increasing distance $d$ decreases capacitance, thereby reducing sensitivity.. Magnetic damping (Option B) is rarely used in electrostatic instruments because the force is purely electrical; air or liquid damping is preferred to avoid interference.. Phase-shifting capacitors (Option A) are used for power factor correction, not for increasing instrument sensitivity.

Answer: C is correct — increasing the area of the plates increases the capacitance $C$, which enhances the rate of change of capacitance $dC/d	heta$, thereby increasing the deflecting torque and the instrument's sensitivity.

Exam Tip: Remember that electrostatic instruments are the only standard meters where the deflecting torque is proportional to the square of the voltage ($V^2$), making them inherently non-linear.

Examoogle · Answer

Option A: using a phase-shifting capacitor

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Option B: using a magnetic damping mechanism

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Option D: increasing the distance between the plates

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