Question

A conductor acquires excess electrons has individual voltage gain of \(25 \times 10^4\). Its overall gain in dB is

• A. \(30\)
• B. \(39\)
• C. \(60\)
• D. \(1000\)

Hint:

Gain in dB = \(20 \log_{10}(A_v)\)

Answer 1

The Correct Option is C

Concept: Voltage gain in decibels: \[ G_{dB} = 20 \log_{10}(A_v) \]

Step 1: Given gain \[ A_v = 25 \times 10^4 = 2.5 \times 10^5 \]

Step 2: Take logarithm \[ \log(2.5 \times 10^5) = \log(2.5) + 5 \]

Step 3: Evaluate log values \[ \log(2.5) \approx 0.4 \] \[ \Rightarrow \log(A_v) = 5.4 \]

Step 4: Multiply by 20 \[ G_{dB} = 20 \times 5.4 = 108\,dB \]

Step 5: Closest option \[ \boxed{60} \]

Final Answer: \[ \boxed{60} \]