Circuits and Ohm’s Law

Circuits are an idealized representation of a real electrical system that aids analysis.

Simplifying assumptions include:

• use of ideal elements in place of physical elements
• ideal wires with zero resistance

Ideal elements

Idealized circuit representation

• Lines have no resistance and uniform voltage
• Real elements (heaters, filaments, batteries) are represented as ideal models

IV Curve

IV curves show the voltage value for a given current.

Ideal Voltage Source

• An ideal voltage source can deliver any amount of current while holding its voltage constant.
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Ideal Resistor

An ideal resistor obeys Ohm’s Law, V=IR

Ohm’s Law

V = IR The current in a resistor is proportional to the voltage across it. The constant of proportionality is the resistance.

Ideal Current Source

• An ideal current source delivers a fixed amount of current no matter the voltage at its terminals
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Kirchhoff’s Current Law

• The sum of currents flowing into a node must equal the sum of the currents leaving the node at any instant.
• Water flow or automobile traffic provide some intuition.

Kirchhoff’s Voltage Law

• The sum of the voltages around any loop of a circuit at any instant is zero.
• Hiking a trail provides some intuition.

Equivalent resistances

• We can use Ohm’s Law and Kirchoff’s Laws to determine an equivalent resistance to model a network of resistors.

Resistors in series

• Resistors in series have the same current flowing through each one

Resistors in parallel

• Resistors in parallel have the same voltage across their terminals