Direct Current Circuits Physics 014 Direct Current Circuits

F P

Topics EMF Resistors RC circuits

Currents and Resistors We get resistance by applying a potential difference V between two points and measuring the resultant current i. (Ohms law)

Circuits To move charges through a resistor we need to establish a potential difference. This is done with an emf device. (A battery)

Circuits emf is an abbreviation for electromotive force

Circuits

Circuits (emf) is an abbreviation for electromotive force An ideal emf device has no internal resistance A real emf device has internal resistance

Circuits How do we calculate the current in a single loop circuit if we know ε & R?

Circuits LOOP RULE: The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero.

Circuits RESISTANCE RULE: For a move through a resistance in the direction of the current, the change in potential is –iR; in the opposite direction +iR

Circuits RESISTANCE RULE: For a move through a resistance in the direction of the current, the change in potential is –iR; in the opposite direction +iR

Circuits Starting at point a, mentally walk clockwise around the circuit until we are back at point a.

Circuits

Circuits Grounding

Multiloop circuits The following is a multiloop circuit. How do we calculate the currents if we know R’s & ε’s. Loop bcdb Branch bcd junction

Multiloop circuits JUNCTION RULE: The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction.

Multiloop circuits

Circuits What equations do the rules give us?

Multiloop circuits Loop badb Loop bdcb Loop adcba

Power In a circuit, the rate at which energy is transferred from a battery to a device is called power.

Power Arbitrary device

Power In terms of potential, resistance and current.

Power The SI unit for power is the Watt (W). 1 W = (1 V) (1 A)

Ammeters and Voltmeters

RC circuits What expressions can be found for resistor-capacitor (RC) combination circuits?

RC circuits

RC circuits What expressions can be found for resistor capacitor combination circuits? Charging the capacitor (a switch) Discharging the capacitor (b switch)

RC circuits Charging: From the loop rule there, solve a differential equation. After rearrangement and plugging in for i

RC circuits Charging: We have the following solution for the differential equation. solution From q we can get these

RC circuits It is useful to define the capacitive time constant

RC circuits

RC Circuits Discharging: From the loop rule, we have the same differential equation without the emf term.

RC circuits Discharging: We have the following solution for the differential equation. solution