Formulas and Theory behind RC Circuits
In a Series Resistor-Capacitor (RC) circuit, the rate at which a capacitor charges or discharges is limited by the resistance present in the circuit. The product of the resistance $R$ and capacitance $C$ defines the **Time Constant** ($\tau$), represented mathematically as:
$$\tau = R \times C$$
Rearranging this equation gives us the primary formula to find the unknown resistance when the time constant and capacitance are known:
$$R = \frac{\tau}{C}$$
Solving via Transient Voltage Equations
When calculating resistance from voltage changes over a known elapsed time ($t$), we use exponential transient equations depending on whether the capacitor is charging or discharging.
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Charging Equation: $V(t) = V_0 \left(1 - e^{-\frac{t}{RC}}\right)$
Rearranged for $R$: $$R = -\frac{t}{C \times \ln\left(1 - \frac{V(t)}{V_0}\right)}$$ -
Discharging Equation: $V(t) = V_0 \times e^{-\frac{t}{RC}}$
Rearranged for $R$: $$R = -\frac{t}{C \times \ln\left(\frac{V(t)}{V_0}\right)}$$
How to Use This Calculator
- Select your calculation mode in **Column 1** (by Time Constant, Charging state, or Discharging state).
- Enter the total capacitance value ($C$) and choose its appropriate unit (e.g., microfarads, nanofarads).
- In **Column 2**, input the necessary timing or voltage parameters depending on the selected method.
- Click the **Calculate Resistance** button in **Column 3**. The calculated unknown resistance value will display at the top of the page above the form.