The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power

The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:

[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]

By rearranging the formula, an homogeneous linear first-order differential equation is found:

[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]

Whose solution has the form of a exponential model:

[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]

The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery. What mathematical function describes this behavior? 1. Exponential2. Linear 3. Quadratic 4. Power

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The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power