How to Calculate the Time Needed for a Condenser Voltage to Decrease by 90%?
What is the relationship between the rate of change of voltage and the voltage in a discharging condenser?
In a discharging condenser, when a condenser discharges electricity, the instantaneous rate of change of the voltage is proportional to the voltage in the condenser. How does this relationship affect the time it takes for the voltage to decrease by a certain percentage?
Explanation:
When a condenser discharges electricity, the instantaneous rate of change of the voltage is proportional to the voltage in the condenser. This relationship can be represented by the equation dV/dt = kV, where dV/dt is the rate of change of voltage, k is a constant, and V is the voltage in the condenser.
To calculate the time needed for the voltage to decrease by 90%, we can use the exponential decay formula V = V₀e^-kt, where V is the voltage at time t, V₀ is the initial voltage, e is the base of the natural logarithm, k is the rate constant, and t is the time.
Given that the instantaneous rate of change of the voltage is -0.01 of the voltage, we have dV/dt = -0.01V. By solving the differential equation and considering the 90% decrease in voltage, we can calculate that it takes approximately 460.52 seconds for the voltage to decrease by 90%.
Detail Explanation:
When a condenser discharges electricity, the instantaneous rate of change of the voltage is proportional to the voltage in the condenser. This is described by the equation dV/dt = kV, where dV/dt represents the rate of change of voltage with respect to time, k is a constant proportionality factor, and V is the voltage in the condenser.
To find the time it takes for the voltage to decrease by a certain percentage, we can use the exponential decay formula V = V₀e^-kt, where V is the voltage at time t, V₀ is the initial voltage, e is the base of the natural logarithm, k is the rate constant, and t is the time it takes for the voltage to decrease.
Given the specific scenario where the instantaneous rate of change of the voltage is -0.01 of the voltage (in volts per second), we can solve the differential equation for the discharging condenser. By considering the 90% decrease in voltage, we can calculate the time needed for the voltage to decrease by 90% to be approximately 460.52 seconds.