Practice problems

Op-amp gain practice problems

An op-amp with two resistors around it makes a signal bigger by a gain the resistors set. These ten problems find the gain both ways round, then the output, then the resistor that gives a gain you want, and end where the output runs out of room at the rails. Type your answer to check it, and open the working whenever you want it.

The method

G = 1 + R_fR_g (non-inverting)

G = − R_fR_in (inverting)

V_out = G × V_in, with the sign: an inverting amp turns + into −
To choose resistors, rearrange: R_f = (G − 1) × R_g non-inverting, R_in = R_f ÷ |G| inverting
The output can't pass its limits, about 1.5 V inside each rail: ±10.5 V on ±12 V rails. Ask for more and it clips

The gain has no unit: it's how many times bigger the output is.

The problems

Type your answer and tap Check. Every one has the working, step by step.

Problem 1 of 10
A non-inverting amplifier has R_f = 33 kΩ and R_g = 10 kΩ. What is its gain?
Show the working
1. A non-inverting amp always adds 1: G = 1 + R_f over R_g.
2. G = 1 + 33 kΩ over 10 kΩ = 1 + 3.3 = 4.3
Answer: 4.3
Problem 2 of 10
An inverting amplifier has R_f = 47 kΩ and R_in = 10 kΩ. What is its gain?
Show the working
1. An inverting amp's gain is G = −R_f over R_in. The minus sign means the output is flipped.
2. G = −47 kΩ over 10 kΩ = −4.7
Answer: −4.7
Problem 3 of 10
A non-inverting amplifier with R_f = 68 kΩ and R_g = 22 kΩ gets 0.4 V in. What is the output voltage?
Show the working
1. G = 1 + 68 kΩ over 22 kΩ ≈ 1 + 3.09 = 4.09
2. V_out = G × V_in = 4.09 × 0.4 V ≈ 1.64 V, the same sign as the input.
Answer: 1.64 V
Problem 4 of 10
An inverting amplifier with R_f = 100 kΩ and R_in = 22 kΩ gets 0.3 V in. What is the output voltage?
Show the working
1. G = −100 kΩ over 22 kΩ ≈ −4.545
2. V_out = −4.545 × 0.3 V ≈ −1.36 V. Positive in, negative out.
Answer: −1.36 V
Problem 5 of 10
You want a non-inverting gain of 8 and have R_g = 4.7 kΩ. What value of R_f gives it?
Show the working
1. From G = 1 + R_f over R_g, the ratio must be G − 1 = 7.
2. R_f = 7 × 4.7 kΩ = 32.9 kΩ. The nearest E12 value, 33 kΩ, gives a gain of about 8.02.
Answer: 32.9 kΩ
Problem 6 of 10
You want an inverting gain of −15 and have R_f = 150 kΩ. What input resistor R_in gives it?
Show the working
1. The size of the gain is R_f over R_in = 15, so R_in = R_f over 15.
2. R_in = 150 kΩ over 15 = 10 kΩ
Answer: 10 kΩ
Problem 7 of 10
A non-inverting amplifier with a gain of 11 runs on ±12 V rails, so its output can reach ±10.5 V. It gets a 0.8 V peak sine. What is the output's peak?
Show the working
1. It would need 11 × 0.8 V = 8.8 V peak.
2. 8.8 V is inside the 10.5 V limit, so nothing clips: the output is a clean 8.8 V peak.
Answer: 8.8 V
Problem 8 of 10
The same amplifier (gain 11, ±12 V rails) now gets a 1.2 V peak sine. What peak does the output actually reach?
Show the working
1. It would need 11 × 1.2 V = 13.2 V peak.
2. The output stops about 1.5 V short of each rail: 12 V − 1.5 V = 10.5 V.
3. 13.2 V is past that, so the tops are cut flat at 10.5 V. The wave clips.
Answer: 10.5 V
Problem 9 of 10
An inverting amplifier with R_f = 220 kΩ and R_in = 10 kΩ runs on ±12 V rails. A steady +0.6 V goes in. What is the output voltage?
Show the working
1. G = −220 kΩ over 10 kΩ = −22, so it would need −22 × 0.6 V = −13.2 V.
2. The bottom limit is 1.5 V above the −12 V rail: −10.5 V.
3. −13.2 V is past it, so the output sits at −10.5 V.
Answer: −10.5 V
Problem 10 of 10
Stretch: a non-inverting amplifier with R_f = 56 kΩ and R_g = 4.7 kΩ runs on ±9 V rails. What is the biggest input peak, in millivolts, that comes out without clipping?
Show the working
1. The output limit is 1.5 V inside the rail: 9 V − 1.5 V = 7.5 V.
2. G = 1 + 56 kΩ over 4.7 kΩ ≈ 12.9
3. V_in = 7.5 V over 12.9 ≈ 0.581 V, which is 581 mV. Any bigger and the tops clip.
Answer: 581 mV

Build it in a free lesson

“Non-inverting amplifiers” is lesson 4 of 6 in Amplifier Peaks, Electronics World 6. Free with an account. Lessons unlock in order, so you’ll do the 38 before it first.

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Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Non-inverting amplifiers” is lesson 4 of 6 in Amplifier Peaks, Electronics World 6. Free with an account. Lessons unlock in order, so you’ll do the 38 before it first.

Or start from the very first lesson, no account needed

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The ideas behind it

Questions people ask

What's the difference between inverting and non-inverting gain?

Non-inverting, G = 1 + Rf ÷ Rg: the output is the right way up and the gain is never below 1. Inverting, G = −Rf ÷ Rin: the output is flipped, and the gain can be any size, even less than 1. The same two resistors give a gain one bigger non-inverting.

Why does my answer clip at 10.5 V and not 12 V?

A classic op-amp's output can't reach its rails. It stops about 1.5 V short of each one, so on ±12 V the output runs from −10.5 V to +10.5 V. A rail-to-rail op-amp gets much closer. If input × gain asks for more, the output sits at the limit.

How do I pick resistors for a gain?

Choose one resistor in kilohms first, often 10 kΩ. Non-inverting, Rf = (G − 1) × Rg. Inverting, Rin = Rf ÷ |G|. Then pick the nearest standard value and check the gain it really gives.