Electric Circuits

Electric Circuits Chapter 18 

Series Circuits • To find the equivalent resistance for resistors in series, use Req = R1 + R2 + R3 + …

Series Circuits • Voltage is shared… current is the same through each resistor • Vtot = V1 + V2 + V3… • IRtot = IR1 + IR2 + IR3 • IRtot = I(R1 + R2 + R3)

Parallel Circuits • To find the equivalent resistance for resistors in parallel, use 1/Req = 1/R1 + 1/R2 + 1/R3 + …

Parallel Circuits • Voltage is the same in each resistor, but current is shared…current branches • Itot = I1 + I2 + I3 + … • V/Req =V/R1 + V/R2 + V/R3 • 1/Req = 1/R1 + 1/R2 + 1/R3

Example • What is the equivalent resistance of three resistors, R1 = 1.0 Ω; R2 = 2.0 Ω and R3 = 3.0 Ω in a) series and b) parallel. What current will be delivered by a 12 V battery in each circuit?

Series and Parallel Combinations • Determine which groups are in series and which are in parallel. • Reduce the circuit by treating equivalent resistances as individual resistors • Find the total current delivered in the circuit • Expand the reduced circuit back to the actual circuit by reversing the steps…

Example • See page 597… Find the current in each resistor.

Kirchhoff’s Rules • Kirchhoff’s rules are used to solve multi-loop circuits… • A point where three or more wires are joined is called a junction. • A path connecting two junctions is called a branch.

Kirchhoff’s Rules

Kirchhoff’s Rules • Kirchhoff’s First Rule – the sum of currents at any junction is zero. The sum of currents entering and leaving a junction is zero. • Kirchhoff’s Second Rule - the sum of potential differences across all elements of a closed loop is zero. The sum of voltage rises and drops in a loop must be zero.

Example • Two resistors are connected in parallel and then connected in series with a third. A battery completes the circuit. a) which resistor carries the most current? b) If R1 = 6.0 Ω, R2 = 3.0 Ω and R3 = 10.0 Ω and the battery’s terminal voltage is 12.0 V, find the current in each resistor and the voltage across each resistor.

Sign Conventions in Kirchhoff’s Rules • When using the loop theorem, when you follow the loop in the direction of voltage increase, V>0. When you follow the loop in the opposite direction, V<0. • When you follow the loop across a resistor in the direction of current, V<0. In a direction opposite to current, V>0.

Sign Conventions in Kirchhoff’s Rules

Example • Series and parallel calculations cannot be used in Figure 18.10 page 603. Instead, use Kirchhoff’s Rules to generate three equations. Use algebra to solve three equations for three unknowns: I1, I2 and I3.

RC Circuits • Circuits with Resistors and Capacitors are called RC circuits. • Initially the capacitor is uncharged so the circuit acts like a voltage – resistor circuit • As the capacitor charges, the charge accumulating on it (and associated negative voltage) reduces the current. • As charge on capacitor increases, current in the circuit decreases.

RC Circuits • Vc = V0[1 - e-t/RC] Where Vc is the voltage across the capacitor and V0 is the battery voltage. • Note t = 0 and t approaches infinity. • Also note t = RC

RC Circuits • I = I0 e-t/RC • I0 is initial current in the circuit • Note t = 0 and t approaches infinity. • Also note t = RC

RC Circuits – Time Constant • Time Constant τ = RC • When t = τ = RC, Vc = 0.63 V0 I = 0.37 I0

Charging and Discharging • In some circuits, the capacitor is continuously charged and discharged. • For discharge, V=V0e-t/RC

Example • In many cameras the built in flash gets its energy from that stored in a capacitor. The capacitor is charged using long life batteries V=9.0V. Once the bulb is fired, the capacitor must recharge quickly through an internal RC circuit. If the capacitor has a value of C = 0.100F, what must the resistance be so the capacitor is charged to 80% of maximum in 5.0 sec?

Ammeters and Voltmeters • An ammeter measures current • A voltmeter measures voltage • Both devices contain a coil of wire attached to a needle inside a magnetic field…a Galvanometer. Due to electromagnetic induction, the presence of a current will cause a needle to deflect. Ammeters and Voltmeters are galvanometers.

Ammeters • Because an ammeter measures current in a circuit loop, all current should travel through the ammeter. Therefore it is placed in series with the circuit. • In order that all current travels through the ammeter, it should have a very small resistance. • An ammeter measures current through a circuit element.

Voltmeter • A voltmeter measures a potential difference across a circuit element. • It is placed in parallel to a circuit element. • In order that the voltmeter not affect the current (and therefore the voltage) in a circuit element, it should have a very high resistance.

Household Wiring • In series, if one element goes out all other elements go out. All elements share the total voltage. • In parallel, if one element goes out the other elements will remain on. All elements have the same voltage. • Is a house wired in series or in parallel?

Household Wiring • Household wiring involves three wires… the ‘hot’ wires have 120V difference between them. These are black and white. • The third wire is a ground wire – connected directly to the ground. It has ZERO potential.

Circuit Breakers • If current in a circuit is too great, the wire or circuit elements can overheat and cause a fire. • Recall extra ‘branches’ in a parallel arrangement reduces the overall resistance. Extra appliances have the same effect…. Current therefore increases. • Circuit breakers limit the amount of current in a loop. The circuit is broken if current is exceeded.

Homework • Read Section 18.5 • Do # 80, 81, 90 – 93, 97 – 100 • Prepare for exam on Chapt 17, 18 • Cathode is negative… it is the electrode at which reduction (gain of electrons) occurs

Electric Circuits