Question

The value of feedback resistor and resistor connected in series with the input signal source are equal to 10k\(\Omega\) and (3)3k\(\Omega\). Calculate the closed loop voltage gain?

• A. -6.7
• B. -33
• C. -13.3
• D. -3.33

Hint:

Inverting Op-Amp Gain. \(A_{cl = -R_f / R_{in\). Check for potential typos in question values if the calculation doesn't exactly match any option.

Answer 1

The Correct Option is D

Assuming this refers to a standard inverting operational amplifier configuration where the feedback resistor is \(R_f\) and the input resistor connected in series with the source is \(R_{in}\)
The closed-loop voltage gain (\(A_{cl}\)) for an ideal inverting amplifier is given by: $$ A_{cl} = -\frac{R_f}{R_{in}} $$ The problem states the values are "equal to 10k\(\Omega\) and (3)3k\(\Omega\)"
It's slightly ambiguous which is which, but standard labelling usually implies \(R_f = 10 \, k\Omega\) and \(R_{in} = (3)3 \, k\Omega\)
$$ A_{cl} = -\frac{10 \, k\Omega}{(3)3 \, k\Omega} \approx -(3)03 $$ This value is not among the options
Let's consider the possibility of a typo in the question or options
If \(R_{in}\) was intended to be \(3 \, k\Omega\) instead of \((3)3 \, k\Omega\): $$ A_{cl} = -\frac{10 \, k\Omega}{3 \, k\Omega} = -\frac{10}{3} \approx -(3)33 $$ This matches option (4)
Assuming the input resistor was intended to be \(3 \, k\Omega\) to match the option