**Q8. The noise voltage (V**_{n})and the signal bandwidth (B) are related as**Options: **a) a) V

_{n} is directly proportional to bandwidth

b) b) V

_{n} is directly proportional to √bandwidth

c) c) V

_{n} is inversely proportional to absolute temperature

d) d) V

_{n} is inversely proportional to bandwidth

Correct Answer: b) V

_{n} is directly proportional to √bandwidth

**Explanation :**Maximum Noise power is given by P

_{n} = V

^{2}/ R

R

_{L} = R, for maximum power transfer from V

_{n} to load resistor R

_{L}In the above figure, according to voltage divider method,

V= V

_{n}/2

P

_{n} = V

^{2}/ R

= (V

_{n}/2)

^{2}/ R

=V

_{n}^{2}/ 4R

V

_{n}^{2}= 4R P

_{n}V

_{n}= √(4R P

_{n})

Noise power P

_{n}= KTB

Where

K = 1.381×10

^{-23} J/K, joules per Kelvin, the Boltzmann constant

B is the bandwidth at which the power P

_{n} is delivered.

T noise temperature

Therefore, V

_{n}= √(4R KTB) or V

_{n} is directly proportional to √bandwidth.