Chapter 32: Fundamentals of Circuits

Circuit Elements and Diagrams

•Circuit Diagram: a logical picture of what is connected to what.

•Light bulbs have two ends and current passes through the bulb; it can be

thought that a light bulb is a resistor that gives off light when a current is

present.

Kirchhoff’s Laws and the Basic Circuit

•Kirchhoff’s Junction Law: the total current into the junction must equal the total

current leaving the junction (∑Iin = ∑Iout).

•Energy Conservation: sum of the potential differences around any loop or

closed path is zero.

•Kirchhoff’s Loop Law: ∆Vloop = ∑(∆V)I = 0

oDraw a circuit diagram.

oAssign a direction to the current.

oTravel around the loop.

∆Vbat = +ε, for an ideal battery in the negative-to-positive

direction.

∆Vbat = -ε, for an ideal battery in the positive-to-negative

direction.

∆VR = -IR for a resistor.

oApply the loop law.

•Complete Circuit: a circuit that forms a continuous path between the battery

terminals.

•Load: a resistor.

•The battery is called the source.

•The potential energy that the charges gain in the battery is subsequently lost

as they “fall through the resistor.

Energy and Power

•Pbat = rate of energy transfer = dU/dt = (dq/dt)ε = Iε, where ε is the emf of a

battery and Pbat has the units of J/s or W.

•Power: the energy transferred per second from the battery’s store of chemicals

to the moving charges that make up the current.

•Energy-Transfer Process: Echem U (potential energy) K (kinetic energy)

Ethermal

•The battery’s chemical energy is transferred to the thermal energy of the

resistors, raising their temperature.

•The potential difference across the resistor is exactly the emf supplied by the

battery, the Pbat and PR are numerically equal (Pbat = PR).

•PR = power dissipated by the resistor = I∆VR = I2R = (∆VR)2/R

•The largest resistance will dissipate most of the power.

•Eth = PR∆t

Series Resistors

•Series Resistors: resistors that are aligned end to end with no junctions

between them.

•The current must be the same through each of these resistors.

•Equivalent Resistance: Req = R1 + R2 + … + RN

•Resistors in series all have the same current (I).