Answer to Question #138325 in Electric Circuits for Ankita

Question

The input voltage to an audio amplifier is 25mV. An oscilloscope connected across a 1MΩ resistor in series with the input to the amplifier indicates 1V peak-to-peak. If the voltage across a 10KΩ load is 3.5V. Determine :
a) the current, voltage and power gains
b) the amplifier's input resistance

Answer 1

Explanations & Calculations

• V_rms value of that applied across the $\small 1M\Omega$ resistor = $\large \frac{V_{p-p}}{2\sqrt2} \small = 0.3536V$
• Therefore, the input current = $\large \frac{0.3536V}{1M\Omega} \small= 0.3536\mu A$
• Current drawn by/ supplied to the load = $\large \frac{3.5V}{10k\Omega} \small = 0.35mA$

• Therefore, the current gain = $\large\frac{I_{out}}{I_{in}} \small=\large\frac{0.35mA}{0.3536\mu A} \small = \large \frac{350\mu A}{0.3536\mu A} \small = \small\bold{989.82}$
• Voltage gain = $\frac{V_{out}}{V_{in}}= \frac{3.5V}{25mV} = \frac{3500mV}{25mV} = \small \bold{140}$

• Power gain = Voltage gain $\small \times$ current gain = $\small 140 \times 989.82 = \bold{1.39\times 10^5}$

• Input resistance = $\large \frac{\text{input voltage}}{\text{input current}} \small = \large \frac{25mV}{0.3536\mu A} \small = \bold{70.701k\Omega}$