Leakage Current in Dielectric & Current-Temp Relation

[coolnish]

1. Is there any formula for calculating the leakage current carried by a dielectric in a capacitor?

2. A battery-powered light bulb has a tungsten filament. When the switch connecting the bulb to the battery is first turned on and the temperature of the bulb is 20 ^\circ {\rm C}, the current in the bulb is 0.860 {\rm A}. After the bulb has been on for 30 {\rm s}, the current is 0.220 {\rm A}.What is then the temperature of the filament?

for number 2, is there any formula relating current to temp ? I looked thru the net and my coursework but found no such formula. Any help for these 2 questions would be greatly appreciated!

 

[KataKoniK]

I can provide some information and guidance on these questions.

1. Yes, there is a formula for calculating the leakage current in a capacitor. It is known as the dielectric absorption current formula and is given by I= C*dV/dt, where I is the leakage current, C is the capacitance, and dV/dt is the rate of change of voltage. This formula is based on the property of dielectric materials to retain some of the charge even after the voltage is removed, which can result in a small current flowing through the capacitor.

2. There is no direct formula that relates current to temperature for a tungsten filament in a light bulb. However, there are some factors that can affect the temperature of the filament, which in turn can affect the current. These factors include the resistance of the filament, the voltage applied, and the heat dissipation from the filament. Based on the given information, it is likely that the increase in temperature of the filament resulted in an increase in resistance, which led to a decrease in current. To accurately determine the temperature of the filament, we would need more information such as the voltage applied and the specific properties of the tungsten filament.

 

[Mene]

1. Yes, there is a formula for calculating the leakage current in a dielectric capacitor. It is given by the equation: I = CVdV/dt, where I is the leakage current, C is the capacitance of the dielectric, and VdV/dt is the rate of change of voltage across the dielectric. This formula is derived from Ohm's law and the concept of capacitance.

2. There is no direct formula relating current to temperature for a tungsten filament in a light bulb. However, there is a relationship between the current and temperature known as the temperature coefficient of resistance. This coefficient describes the change in resistance of a material with respect to temperature. In this case, the temperature coefficient of resistance for tungsten is positive, meaning that as the temperature increases, so does the resistance. Therefore, the decrease in current from 0.860 A to 0.220 A after 30 seconds indicates an increase in resistance and thus a higher temperature of the filament. To calculate the exact temperature, you would need to know the initial resistance of the filament and use the equation R = V/I, where R is the resistance, V is the voltage, and I is the current. You can then use the temperature coefficient of resistance to determine the change in temperature.