Static and Dynamic Characteristics

Static performance is specified when the measurand is constant: accuracy is closeness to the true value, precision is repeatability, sensitivity is the slope Δoutput/Δinput, and resolution is the smallest change detectable. Hysteresis is the difference in reading for increasing versus decreasing input.

Dynamic performance matters for time-varying inputs. A first-order instrument (thermometer, RC sensor) responds as 1 − e^(−t/τ); a second-order instrument (galvanometer, accelerometer) is characterised by ζ and ω_n like a control system.

Relation 1 —

Write this relation with symbols exactly as in A Course in Electrical & Electronic Measurements — AK Sawhney before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

Write this relation with symbols exactly as in A Course in Electrical & Electronic Measurements — AK Sawhney before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

Write this relation with symbols exactly as in A Course in Electrical & Electronic Measurements — AK Sawhney before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

A first-order instrument reaches 63.2% of a step change in one time constant τ and is essentially settled after 5τ. The dynamic error for a ramp input is proportional to τ, so a fast sensor needs a small τ.

Loading effect: a voltmeter of finite resistance draws current and lowers the measured voltage; the error shrinks as the meter impedance rises relative to the circuit. Always check the loading correction for high-impedance sources.

Sensitivity and resolution are distinct: high sensitivity (large slope) does not guarantee fine resolution if noise or quantisation limits the smallest detectable change.

State assumptions explicitly before using any relation for static and dynamic characteristics — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Instrumentation viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Instrumentation papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to static and dynamic characteristics.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Static and Dynamic Characteristics appears in process control and labs. In Indian electrical curricula this topic is tested because it connects theory to measurement and transducers.

GATE and semester exams often combine static and dynamic characteristics with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use static and dynamic characteristics?" — answer with a lab, mini-project, or plant visit example if possible.

• Confusing accuracy (closeness to true value) with precision (repeatability)
• Ignoring loading effect for high source impedance
• Using 5τ as the time constant instead of the settling time
• Treating sensitivity and resolution as the same thing

Before attempting static and dynamic characteristics problems, confirm you can:

1. Static: linearity, hysteresis, dead zone, threshold
2. Dynamic: time constant τ, rise time, settling time
3. Loading effect: instrument impedance affects measured system

Revise the solved examples in A Course in Electrical & Electronic Measurements — AK Sawhney and one previous-year GATE or university paper for this unit.