Question

Consider a parallel plate capacitor with capacitance 2μF that, initially, when fully charged up, has an electric field with magnitude Eo = 90 V/m (assume the capacitor is disconnected from any power supplies after it is charged). At time t=0 the capacitor is hooked to a 2 MΩ resistor.

Sketch a plot of the electric field between the plates versus time.

Answer 1

The electric field between the plates of a parallel plate capacitor connected to a 2 MΩ resistor decreases exponentially over time, reflected in an exponential decay graph towards zero.

Step-by-step explanation:

The student is asking about the discharge of a charged parallel plate capacitor which is connected to a 2 MΩ resistor. The initial electric field between the plates of the capacitor is given as Eo = 90 V/m. Upon connection with the resistor, the charge starts to decrease exponentially over time, which in turn, causes the electric field to decrease exponentially. This is because the electric field (E) in a parallel plate capacitor is directly proportional to the surface charge density (σ), which in turn is proportional to the charge Q (σ = Q/A where A is the area of the plates). Therefore, as Q decreases over time, E decreases as well. The graph of the electric field versus time would show an exponential decay towards zero.