Week 4 Introduction In conventional English A circuit is a path or route that starts at one place and ultimately returns to that same place In electronics a circuit is a closed path through which electrical current can ow Three parts of the ashlight comprise the circuit The battery supplies the power The bulb produces light when connected to the power The switch which can either be on meaning it is connected or off meaning it is disconnected When the switch is open there is no path for current to ow Electrical circuits are made up of components such as resistors capacitors inductors and transistors connected together by wires Electrical Circuits Our electrical abstraction is based on two major types of pieces nodes and components In general a circuit consists of several components connected by nodes Voltage is a difference in electrical potential between two different nodes in a circuit Ground node is the point on a circuit that we pick to use as reference Voltage is a relative concept so we can pick any point in the circuit and call it ground Current is a ow of electrical charge through a path in the circuit Positive charge carriers owing in a certain direction correspond to positive current owing in that direction Voltages propel electrical currents A voltage can be associated with every node in a circuit and its the difference between the voltages at two nodes that causes electrical currents to ow between those two nodes It is the difference in voltage between two nodes that drives electrical current between the nodes Nodes Components Component Types Voltage Source Current Source Resistor Multiple Components Kirchhoff s Current Law Example Kirchhoff s Voltage Law Series Combination Parallel Combination A node is any electrically connected region in space such as a wire a piece of metal or several connected wires For practical purposes we can think about a node as a set of point in a circuit that are all connected by only a wire A component describes relationships between nodes as well as the way that current ows between nodes In general a component is anything that connects to multiple nodes Each component has some special characteristics that govern the relationship between its voltage and its current Example the variable v represents the potential difference between the two nodes on either side of the component In particular because the plus sign is on the top node v represents the potential difference between the top node and the bottom node In the picture i represents the current owing through the component in the direction indicated by the arrow Each electrical component imposes a relation between the voltage difference of its two nodes and on the current owing through it This relation is called a constitutive relation A voltage source is a component whose voltage is a constant independent of the current owing through it A voltage source will make sure that the potential difference between its top node and its bottom node is always the indicated voltage A current source is a component whose current is a constant independent of the voltage across it A current source will make sure that the current owing through it is always the indicated current The relationship between voltage and current is Ohm s Law V IR When multiple components exist in the same circuit each exerts its own constraints on the currents and node voltages in the circuit KCL states that the sum of all currents owing out of a node must be zero For the top node we can say that i1 i2 i3 0 For the bottom node we can say that i1 i2 i3 0 KVL states that for any complete loop in a circuit the that component voltage encountered when traversing that loop must be zero Components are considered to be connected in series if they share one node that is not shared with another component In series current is constant Two resistors in series can be replaced with a single resistor to yield an equivalent circuit Components are considered to be connected in parallel if there exists a closed loop containing only these two components In parallel voltage is constant Two resistors in parallel can be replaced with a single resistor to yield an equivalent circuit
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