amplifier

[logistic_guy]

A voltage amplifier delivers \(\displaystyle 200 \ \text{mV}\) across a load resistance of \(\displaystyle 1 \ \text{k}\Omega\). It was found that the output voltage decreased by \(\displaystyle 5 \ \text{mV}\) when \(\displaystyle R_L\) decreased to \(\displaystyle 780 \ \Omega\). What are the values of the open-circuit output voltage and the output resistance of the amplifier?

 

[khansaheb]

A voltage amplifier delivers \(\displaystyle 200 \ \text{mV}\) across a load resistance of \(\displaystyle 1 \ \text{k}\Omega\). It was found that the output voltage decreased by \(\displaystyle 5 \ \text{mV}\) when \(\displaystyle R_L\) decreased to \(\displaystyle 780 \ \Omega\). What are the values of the open-circuit output voltage and the output resistance of the amplifier?

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[logistic_guy]

A voltage amplifier delivers \(\displaystyle 200 \ \text{mV}\) across a load resistance of \(\displaystyle 1 \ \text{k}\Omega\). It was found that the output voltage decreased by \(\displaystyle 5 \ \text{mV}\) when \(\displaystyle R_L\) decreased to \(\displaystyle 780 \ \Omega\). What are the values of the open-circuit output voltage and the output resistance of the amplifier?

Let \(\displaystyle V_L\) be the output voltage, then

\(\displaystyle V_L = V\frac{R_L}{R_T + R_L}\)

where \(\displaystyle V\) is the open circuit voltage and \(\displaystyle R_T\) is the Thevenin resistor (the amplifier resistor).

 

[logistic_guy]

\(\displaystyle V_L = V\frac{R_L}{R_T + R_L}\)

Plug in numbers.

\(\displaystyle 0.2 = V\frac{1000}{R_T + 1000}\)

 

[logistic_guy]

Plug in numbers.

\(\displaystyle 0.2 = V\frac{1000}{R_T + 1000}\)

We also have:

\(\displaystyle 0.195 = V\frac{780}{R_T + 780}\)

 

[logistic_guy]

\(\displaystyle 0.195 = V\frac{780}{R_T + 780}\)

Solve for \(\displaystyle V\).

\(\displaystyle V = 0.195\left(\frac{R_T + 780}{780}\right)\)

 

[logistic_guy]

\(\displaystyle V = 0.195\left(\frac{R_T + 780}{780}\right)\)

Substitute this result in the first equation.

\(\displaystyle 0.2 = V\frac{1000}{R_T + 1000}\)


\(\displaystyle 0.2 = 0.195\left(\frac{R_T + 780}{780}\right)\frac{1000}{R_T + 1000}\)

 

[logistic_guy]

\(\displaystyle 0.2 = 0.195\left(\frac{R_T + 780}{780}\right)\frac{1000}{R_T + 1000}\)

If we solve for \(\displaystyle R_T\), we get:

the output resistance of the amplifier?

\(\displaystyle R_T = \textcolor{blue}{100 \ \Omega}\)