Question

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

Answer 1

Answer:

1. Exponential

Step-by-step explanation:

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:

$C \cdot \frac{dV}{dt} + \frac{V}{R} = 0$

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

$\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0$

Whose solution has the form of a exponential model:

$V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }$