Rc Circuits
RC Circuits
•In this presentation, circuits with multiple batteries, resistors and capacitors will be reduced to an equivalent system with a single battery, a single resistor, and a single capacitor. Kirchoff 's laws will be stated, and used to find the currents in a circuit. In addition, the equation for the time-constant of an RC circuit will be derived.
Ohm 's Law
When a battery is connected to a resistor, the battery will cause a current to flow through the resistor. The larger the voltage and smaller the resistance the greater the current.
V = IR
More Concepts
Current is the rate of flow of charge around a circuit.
dQ What actually flows in a circuit is electrons, but electrons are I= negatively charged and current is positive. The current always dt points the opposite direction as the electrons. The unit of Current is the Ampere and is defined to be one coulomb per second.
Resistivity
The resistance of a resistor depends on both the material the resistor is made of and the geometry of the resistor. The longer the resistor the greater the distance electrons must travel and the more times they can collide with other objects. The longer the material the greater the resistance. The wider the resistor the larger the path. A wider resistor is like a wider road or a larger pipe it allows more room and easier flow. The resistance is inversely proportional to the cross-sectional area of the resistor. The resistance is equal to the resistivity of the material, times the length of the resistor, divided by the cross-sectional area of the resistor. ρ∗ l R= A
Resistorsresistors placed end to end In Series Image two identical so that they become one resistor. These two resistors have the same cross-sectional area and same resistivity but double the length of a single resistor. Therefore this resistor has double the resistance of one of the original resistors. This motivates the way in which resistances in series add together. We can
•In this presentation, circuits with multiple batteries, resistors and capacitors will be reduced to an equivalent system with a single battery, a single resistor, and a single capacitor. Kirchoff 's laws will be stated, and used to find the currents in a circuit. In addition, the equation for the time-constant of an RC circuit will be derived.
Ohm 's Law
When a battery is connected to a resistor, the battery will cause a current to flow through the resistor. The larger the voltage and smaller the resistance the greater the current.
V = IR
More Concepts
Current is the rate of flow of charge around a circuit.
dQ What actually flows in a circuit is electrons, but electrons are I= negatively charged and current is positive. The current always dt points the opposite direction as the electrons. The unit of Current is the Ampere and is defined to be one coulomb per second.
Resistivity
The resistance of a resistor depends on both the material the resistor is made of and the geometry of the resistor. The longer the resistor the greater the distance electrons must travel and the more times they can collide with other objects. The longer the material the greater the resistance. The wider the resistor the larger the path. A wider resistor is like a wider road or a larger pipe it allows more room and easier flow. The resistance is inversely proportional to the cross-sectional area of the resistor. The resistance is equal to the resistivity of the material, times the length of the resistor, divided by the cross-sectional area of the resistor. ρ∗ l R= A
Resistorsresistors placed end to end In Series Image two identical so that they become one resistor. These two resistors have the same cross-sectional area and same resistivity but double the length of a single resistor. Therefore this resistor has double the resistance of one of the original resistors. This motivates the way in which resistances in series add together. We can
References: Ohanian, Hans C., and John T. Markert. Physics for Engineers and Scientists. New York: W.W. Norton, 2007. Print.