Electric Circuits Just like we can use pipes to carry water, we can use wires to carry electricity. We can use this concept to understand electric circuits. The flow of water through pipes is caused by pressure differences, and the flow is measured by volume of water per time. The flow of electricity is cause by a voltage or electro potential difference and the flow or current is measure by the flow of charge per time amperage.

Voltage PEel = k q1 q2 / r12 Vat 2 due to 1 = PEof 2 / q2 In electricity, the concept of voltage will be like pressure. Water flows from high pressure to low pressure (this is consistent with the analogy that Voltage is like height since DP = rgh for fluids) ; electricity flows from high voltage to low voltage. PEel = k q1 q2 / r12 Vat 2 due to 1 = PEof 2 / q2 volt = Joule / Coulomb

Voltage Sources: batteries and power supplies A battery or power supply supplies voltage. This is analogous to what a pump does in a water system.

Current Charges flows in electricity. How do we measure this flow? By Current: current = I = Dq / Dt UNITS: Amp(ere) = Coulomb / second

Circuit Elements In this first part of the course we will consider two of the common circuit elements: capacitor resistor The capacitor is an element that stores charge for use later (like a water tower). - Example UPS, TVs The resistor is an element that “resists” the flow of electricity. - There are resistors, Light bulbs, stovers and so on.

Capacitance We define capacitance as the amount of charge stored per volt: C = Qstored / DV. UNITS: Farad = Coulomb / Volt Just as the capacity of a water tower depends on the size and shape, so the capacitance of a capacitor depends on its size and shape. Just as a big water tower can contain more water per foot (or per unit pressure), so a big capacitor can store more charge per volt.

Two basic ways There are two basic ways of connecting two capacitors: series and parallel. In series, we connect capacitors together like railroad cars; using parallel plate capacitors it would look like this: + - + - high V low V C1 C2 1/CEffective Series = 1/C1 + 1/C2 =

Series If we include a battery as the voltage source, the series circuit would look like this: C1 + Vbat C2 Note that there is only one way around the circuit, and you have to jump BOTH capacitors in making the circuit - no choice!

Parallel In a parallel hook-up, there is a branch point that allows you to complete the circuit by jumping over either one capacitor or the other: you have a choice! High V C1 Low V C2

Parallel Circuit If we include a battery, the parallel circuit would look like this: + + + Vbat C1 C2 Ceff = C1 + C2 .

Review of Formulas For capacitors in SERIES we have: 1/Ceff = 1/C1 + 1/C2 . For capacitors in PARALLEL we have: Ceff = C1 + C2 . Note that adding in series gives Ceff being smaller than the smallest, while adding in parallel gives Ceff being larger than the largest!

Resistance Electrical Resistance - anything in a circuit that slows the flow of electrons down  Current is somewhat like fluid flow. Recall that it took a pressure difference to make the fluid flow due to the viscosity of the fluid and the size (area and length) of the pipe. So to in electricity, it takes a voltage difference to make electric current flow due to the resistance in the circuit.

Resistance By experiment we find that if we increase the voltage, we increase the current: V is proportional to I. The constant of proportionality we call the resistance, R: V = I*R Ohm’s Law UNITS: R = V/I so Ohm = Volt / Amp.

Electrical Power The electrical potential energy of a charge is: PE = q*V . Power is the change in energy with respect to time: Power = DPE / Dt . Putting these two concepts together we have: Power = D(qV) / Dt = V(Dq) / Dt = I*V. P = I2*R = V2/R = I*V

Connecting Resistors There are two basic ways of connecting two resistors: series and parallel. In series, we connect resistors together like railroad cars; this is just like we have for capacitors: + - + - high V low V R1 R2

Formula for Series: To see how resistors combine to give an effective resistance when in series, we can look either at V = I*R, or at R = rL/A . Reff = R1 + R2. R1 I V1 + R2 Vbat V2 -

Formula for Parallel Resistors The result for the effective resistance for a parallel connection is 1/Reff = 1/R1 + 1/R2 . . Itotal + Vbat I1 R1 R2 I2 -

Review: Capacitors: C = Q/V Resistors: V = IR PE = ½CV2; C// = KA/[4pkd] Series: 1/Ceff = 1/C1 + 1/C2 Parallel: Ceff = C1 + C2 series gives smallest Ceff, parallel gives largest Resistors: V = IR Power = IV; R = rL/A Series: Reff = R1 + R2 Parallel: 1/Reff = 1/R1 + 1/R2 series gives largest Reff, parallel gives smallest