What does the thermal noise generated by a resistor depend upon?
Correct Answer: Both its resistance value and its operating temperature
Introduction / Context:Quantifying resistor noise helps engineers choose components for preamplifiers, mixers, and precision measurement equipment. Thermal noise is an unavoidable physical phenomenon.
Given Data / Assumptions:
- Resistor with value R operating at absolute temperature T.
- Observation bandwidth B.
- No additional excess noise mechanisms (e.g., flicker).
Concept / Approach:
The mean-square thermal noise voltage across a resistor is v_n^2 = 4kTRB. Thus, thermal noise magnitude increases with both resistance R and absolute temperature T, and also with bandwidth B.
Step-by-Step Solution:
Start with Johnson–Nyquist relation: v_n^2 = 4kTRB.Holding bandwidth constant, v_n rises as R or T increases.Therefore both resistance and temperature are determinants of the noise.Verification / Alternative check:
Practical lab measurements show doubling the resistance or doubling the absolute temperature increases the noise voltage accordingly (by sqrt(2) in RMS for each doubling).
Why Other Options Are Wrong:
- Only R or only T: incomplete; both contribute.
- Neither: contradicts physics.
- Only DC voltage: thermal noise exists even with zero DC bias.
Common Pitfalls:
- Ignoring the bandwidth term B, which also scales noise.
Final Answer:
Both its resistance value and its operating temperature