RC Circuit Diagram
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An RC circuit diagram shows a resistor (R) and capacitor (C) connected together, either in series or parallel, with a voltage or current source. The key parameter is the time constant τ = RC, which determines how quickly the capacitor charges or discharges. RC circuits appear everywhere in electronics as filters, timing networks, integrators, differentiators, and coupling elements.
A series RC circuit driven by a step voltage source VS exhibits an exponential charging response. When the switch closes at t = 0, current flows through R and into C. The capacitor voltage rises toward VS following: Vc(t) = VS × (1 − e^(−t/τ)), where τ = RC is the time constant. At t = τ, the capacitor has reached 63.2% of VS. After 5τ, it is considered fully charged (99.3%).
Discharging: With the source removed and the capacitor discharging through R, the voltage falls as: Vc(t) = V0 × e^(−t/τ), where V0 is the initial voltage. At t = τ, 36.8% of the initial voltage remains.
Current during charging: The capacitor starts as a short circuit (I = VS/R) and the current decays exponentially: I(t) = (VS/R) × e^(−t/τ). At full charge, I = 0.
Phase relationship in AC circuits: In a series RC circuit with a sinusoidal source, the voltage across C lags the source voltage by a phase angle φ = arctan(−1/(ωRC)), where ω = 2πf is the angular frequency. The impedance of the capacitor is ZC = 1/(jωC) = −j/(ωC).
Low-pass RC filter: Output taken across C. At low frequencies, XC = 1/(ωC) is large and most voltage appears across C (passes). At high frequencies, XC is small and the voltage is dropped mainly across R. The cut-off (−3 dB) frequency is fc = 1/(2πRC). The transfer function is H(jω) = 1/(1 + jωRC). Above fc, the output rolls off at −20 dB/decade.
High-pass RC filter: Output taken across R. At low frequencies, XC is large and most voltage is dropped across C (blocks). At high frequencies, XC is small and the output across R equals approximately the input. The same cut-off frequency fc = 1/(2πRC) applies. Below fc, the output rolls off at −20 dB/decade.
Integrator: With a large RC time constant (τ >> signal period), the circuit output (taken across C) approximates the integral of the input: Vc ≈ (1/RC) ∫Vin dt. Used in analog computation and waveform shaping.
Differentiator: With a small RC time constant (τ << signal period), the circuit output (taken across R) approximates the derivative of the input: VR ≈ RC × dVin/dt. Used to detect edges in digital waveforms and in trigger circuits.
Design example — 1 kHz low-pass filter: Choose C = 100 nF. Then R = 1/(2π × 1000 × 100×10^−9) = 1/(6.283×10^−4) ≈ 1.59 kΩ → use 1.6 kΩ standard.
Energy stored in capacitor: E = ½CV², where V is the voltage across the capacitor at time t. This energy is released when the capacitor discharges.
RC timing circuits: RC networks are used to set delay times in monostable multivibrators, 555 timer circuits (the 555 timer's timing capacitor charges through a resistor network), debounce filters for mechanical switch contacts, and power-on-reset (POR) circuits in microcontrollers.
You can design and visualise RC charging, discharging, and filter circuits using the free circuit diagram editor at circuitdiagrammaker.com — place an R and C, add a voltage source, and trace the voltage response across each component.
How to wire rc circuit diagram
- Define the application requirement Decide whether you need a low-pass filter (smooth signals), high-pass filter (block DC/low frequencies), timing network, or coupling capacitor, and note the target frequency or time constant.
- Calculate RC using the time constant or frequency For timing: τ = RC = desired time. For filtering: fc = 1/(2πRC), so RC = 1/(2πfc). Fix one component value and solve for the other.
- Select standard component values Choose the nearest E24 or E96 resistor value and a standard capacitor value (1 nF, 10 nF, 100 nF, 1 μF, etc.) that gives the closest τ or fc.
- Wire the circuit For a low-pass filter: connect R in series between Vin and the output node, then connect C from the output node to GND. Take Vout across C.
- Verify the cut-off frequency Apply a sinusoidal signal and sweep the frequency. At fc, measure that Vout = Vin / √2 (−3 dB, approximately 70.7% of Vin).
- Check phase shift At fc, the output should lag the input by 45° for a low-pass filter. Use an oscilloscope to verify by comparing the zero crossings.
- Adjust if needed If the measured fc differs, use a 1% tolerance resistor and a precise capacitor (film type, not ceramic X7R if accuracy matters).
Specifications
| Time constant formula | τ = R × C (seconds, when R in Ω and C in Farads) |
|---|---|
| Capacitor voltage (charging) | Vc(t) = VS × (1 − e^(−t/RC)) |
| Capacitor voltage (discharging) | Vc(t) = V0 × e^(−t/RC) |
| Current during charging | I(t) = (VS/R) × e^(−t/RC) |
| Voltage at t = τ (charging) | 63.2% of VS |
| Voltage at t = 5τ (charging) | 99.3% of VS (considered fully charged) |
| Cut-off frequency (low-pass / high-pass) | fc = 1 / (2π × R × C) |
| Capacitor impedance (AC) | ZC = 1 / (jωC) = −j / (ωC) |
| Phase shift (low-pass output) | φ = −arctan(ωRC) degrees (output lags input) |
| Rolloff above/below fc | −20 dB/decade (−6 dB/octave) |
Safety warnings
- Electrolytic capacitors are polarised — always connect the positive terminal to the higher voltage node; reverse polarity causes gas build-up and can rupture the capacitor.
- High-voltage capacitors can store dangerous charge — before handling, discharge through a bleed resistor (e.g. 10 kΩ, 1 W) rated for the circuit voltage.
Tools needed
- Resistor (value chosen from RC formula)
- Capacitor (film or ceramic, value chosen from RC formula)
- DC regulated power supply or signal generator
- Oscilloscope (to observe charging curves and phase shift)
- Digital multimeter or LCR meter (to verify component values)
- Breadboard and connecting wires
Common mistakes
- Using the wrong capacitor type (e.g. electrolytic with wrong polarity, or Y5V ceramic) causing inaccurate timing or filter frequency.
- Connecting the output across R for a low-pass filter instead of across C — this gives a high-pass response, the opposite of what is needed.
- Ignoring the source and load impedances: the source impedance adds to R and the load impedance is in parallel with C, both shifting the actual fc from the calculated value.
- Selecting component values that result in excessive power dissipation in R — remember that at DC, the capacitor is fully charged and no current flows; power is only dissipated during transients.
Troubleshooting
- Measured cut-off frequency is significantly different from calculated
- Cause: Actual capacitor value differs from nominal due to tolerance, or source and load impedances are shifting the effective R. Fix: Measure the capacitor value with an LCR meter. Add source resistance to R in the formula and account for load resistance in parallel with C.
- Oscilloscope shows slow charging that never reaches full voltage
- Cause: The RC time constant is too large for the measurement window, or the signal source is limiting current. Fix: Reduce R or C to shorten τ, or extend the oscilloscope time base. Verify the source can supply enough current.
- Filter passes noise above the expected cut-off frequency
- Cause: Stray inductance of R or parasitic resonance with C bypasses the filter at very high frequencies. Fix: Use a surface-mount resistor with minimal lead inductance; for RF filtering, use a dedicated LC or ferrite bead filter.
Frequently asked questions
What is the time constant of an RC circuit diagram?
The time constant τ = RC (in seconds, with R in ohms and C in farads) defines how quickly the capacitor charges or discharges. After one time constant, the capacitor reaches 63.2% of the final voltage; after five time constants it is essentially fully charged (99.3%).
What is the difference between an RC low-pass and high-pass filter?
In a low-pass RC filter, the output is taken across the capacitor, passing low frequencies and attenuating high ones. In a high-pass filter, the output is taken across the resistor, passing high frequencies and blocking low ones and DC. Both share the same cut-off frequency fc = 1/(2πRC).
How do I calculate the cut-off frequency of an RC circuit?
The cut-off (−3 dB) frequency is fc = 1 / (2π × R × C). For example, with R = 10 kΩ and C = 1 nF: fc = 1 / (2π × 10000 × 1×10^−9) ≈ 15.9 kHz.
Why does the capacitor voltage not rise instantly in an RC circuit?
The resistor limits the current flow into the capacitor. Since I = C × dV/dt, a finite current means a finite rate of voltage rise, resulting in the exponential charging curve Vc(t) = VS(1 − e^(−t/RC)).
What is an RC integrator circuit?
When τ = RC >> signal period, the capacitor cannot fully charge and the output voltage is approximately the integral of the input: Vc ≈ (1/RC)∫Vin dt. This is used for waveform conversion, such as turning a square wave into a triangular wave.
What capacitor type should I use in an RC filter?
For precision filters, use film capacitors (polyester, polypropylene) which have stable values and low loss. For decoupling and general timing, ceramic capacitors (X7R or C0G/NP0) are fine. Avoid Y5V ceramics for timing circuits as their capacitance changes drastically with voltage and temperature.
Can an RC circuit be used as a differentiator?
Yes. When τ = RC << signal period, the resistor voltage VR ≈ RC × dVin/dt, making the circuit a differentiator. The output across R produces sharp spikes at signal transitions, useful for edge detection in digital circuits.