Convert the input voltage to Volts.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Convert the input voltage to Volts.
$$V_{in} = 120 \text{ mV} = 120 \times 10^{-3} \text{ V} = 0.120 \text{ V}$$
The output voltage is given as $V_{out} = 6 \text{ V}$.
Step 2: Calculate the voltage gain in decibels using the formula:
$$A_{V,dB} = 20 \log_{10} \left( \frac{V_{out}}{V_{in}} \right)$$
Substitute the values:
$$A_{V,dB} = 20 \log_{10} \left( \frac{6 \text{ V}}{0.120 \text{ V}} \right)$$
Step 3: Perform the division inside the logarithm.
$$A_{V,dB} = 20 \log_{10} (50)$$
Step 4: Calculate the logarithm and multiply by 20.
$$A_{V,dB} = 20 \times 1.69897$$
$$A_{V,dB} = 33.9794 \text{ dB}$$
Rounding to two decimal places:
$$A_{V,dB} \approx 33.98 \text{ dB}$$
The voltage gain of the amplifier in decibels is $\boxed{\text{33.98 dB}}$.
