Ohm's Law
V = I × RSolve voltage, current, or resistance from the other two values.
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Ohm's Law
Solve voltage, current, or resistance from the other two values.
V = I × R
VoltageCalculated
12 V
Calculation steps
1Unknown selected: V
2Rearrange: V = I × R
3Substitute the known values to obtain V = 12 V
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Five guided tools with their own pages, worked examples and lessons. New to electronics? Follow a guided learning path.
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34guided lessons
Operational Amplifiers
Learn why an op-amp tries to make its two input voltages equal and how that creates useful amplifiers.
Mental model
Think of the op-amp as an extremely sensitive controller. It watches the difference between + and − inputs, then moves its output hard enough to reduce that difference.
01
An operational amplifier starts with an enormous open-loop voltage gain. Even a tiny difference between its two inputs would command a very large output, so using it without feedback usually drives the output into saturation.
02
Negative feedback returns part of the output to the inverting input. The output then settles at the value that makes the input difference extremely small. This is the origin of the useful approximation V+ ≈ V−; it is a consequence of feedback, not a universal property.
03
Always check the non-ideal limits after calculating the ideal answer: input common-mode range, output swing, gain-bandwidth product, slew rate and output current.
Why it matters
Op-amps appear in sensor conditioning, filters, control loops, audio circuits and ADC interfaces. Understanding feedback lets you analyze many different circuits with the same two ideal rules.
Core ideas
- The input current is approximately zero in an ideal op-amp.
- With negative feedback, V+ ≈ V− while the output stays inside the supply rails.
- The surrounding resistors—not the huge open-loop gain—set the useful closed-loop gain.
Key equations
Inverting: Av = −Rf / RinNon-inverting: Av = 1 + Rf / RgEXAMPLE
Worked example — non-inverting amplifier
1Given: Rf = 9 kΩ, Rg = 1 kΩ and Vin = 0.20 V.
2Gain: Av = 1 + 9/1 = 10.
3Output: Vout = 10 × 0.20 = 2.0 V.
4Check: a 2.0 V output must be possible with the chosen supply voltage.
Common mistake
Do not assume V+ equals V− when there is no negative-feedback path or when the output has already saturated.
RememberThe input current is approximately zero in an ideal op-amp.
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More than an answer
- 1Identify the variablesSeparate the known values from what you need to find.
- 2Check the unitsConvert values to V, A, Ω and F before calculating.
- 3Follow the workingCompare each step with your own solution.