Circuit Electricity
The following symbols are used in electric circuits:
Four devices are commonly used in the laboratory to study Ohm s law: the battery, the voltmeter, the ammeter and a resistance. The ammeter and voltmeter measure current and voltage respectively. Ammeter measures current through the battery, the filament, and itself. Placed in series This arrangement measures the voltage across the battery. Placed in parallel.
Resistors are loads in a circuit. They are the things you turn on. For labs we can insert resistors of known resistance. They are color coded..
Circuits: 3 components Voltage Source (Battery) Conductor (Wire for Current to flow) Resistor (Load or item being turned on )
2 General Types of Circuits Series Parallel
RESISTORS IN SERIES To wire in SERIES means to make a circuit with a single pathway for the current.
An equivalent resistance (R E ) is the resistance of a single resistor that could replace all the resistors in a circuit. The single resistor would have the same current through it as the resistors it replaced. RULES FOR RESISTORS IN SERIES Voltage Adds V T = V 1 + V 2 + V 3 In a series circuit, the sum of the voltage drops equal the voltage drop across the entire circuit. Current is constant I T = I 1 = I 2 = I 3 Resistance Adds R E = R 1 + R 2 + R 3
Example1: Two resistances of 2 Ω and 4 Ω respectively are connected in series. If the source of emf maintains a constant potential difference of 12 V, a. What is the current delivered to the external circuit? Re = R 1 + R 2 = 2 + 4 = 6 Ω I T V R e 12 6 = 2 A b. What is the potential drop across each resistor? V 1 = I R 1 = 2(2) = 4 V V 2 = I R 2 = 2(4) = 8 V
1 2 3 4 TOTAL Voltage Current Resistance
RESISTORS IN PARALLEL To wire in PARALLEL means to make a circuit with multiple pathways for the current.
RULES FOR RESISTORS IN PARALLEL Voltage is Constant V T = V 1 = V 2 = V 3 The voltage drop across each branch is equal to the voltage of the source. Current Adds I T = I 1 + I 2 + I 3 Each resistor provides a new path for electrons to flow. The total current is the sum of the currents through each resistor. 1 1 1 1 Reciprocals of Resistance Adds R R R R The equivalent resistance of a parallel circuit decreases as each new resistor is added. E 1 2 3
Example: A 5Ω and 10Ω resistor are wired in parallel to 6V battery. A. What is their equivalent resistance? R 1 = 5Ω R 2 = 10Ω V= 6V 1 = 1 + 1 R T 5 10 R T = 3.33 Ω B. What is the current through each resistor? I I V R V R = 6 V 5 Ω = 6 V 10 Ω = 1.2 A = 0.6 A I T = 1.80A I V R = 6 V 3.33Ω I T = 1.80A
Total 1 2 Voltage Current Resistance
Why can a bird stand on a high voltage wire and not get shocked? Because there is no Potential difference between his feet. Will either bird get shocked now? Yes, the one over the light bulb, because a potential difference exists between his feet.
A word about Electrical Safety If not Ground plugs. One end of the ground plug is connected to the appliance cover. The wall jack which receives the ground plug is connected to the ground, so any charge leaking onto the appliance will drain to ground not you. You are the path of least resistance..
One milliampere: tingling sensation Ten milliamperes: nerves and muscles overloaded 200 milliamperes: potentially fatal; heart fibrillation 500-1000 milliamperes: not necessarily fatal; heart will restart One ampere or more: burn alive
As more and more appliances are added to a circuit in parallel the resistance decreases and the current increases. Too much current can result in an overload and a possible fire. Fuses and Circuit breakers are used to prevent overload, by limiting the amount of current that can flow through a circuit. A fuse uses a thin metal wire or ribbon that melts when current through it is too high. These must be replaced.
Houses today use CIRCUIT BREAKERS. These do not need to be replaced and use a bimetallic strip that trips a switch. Brass expands more than steel As temperature increases, the bimetallic strip arcs to the left, settles into groove, and the spring pulls the metal bar down breaking the circuit.
How can we solve complex circuits? That is circuits that have both parallel and series components? We will use Equivalent Resistance
Equivalent Resistance simplifies a circuit by replacing resistor sets with a single EQUAL resistor For example: The 8Ω and 4Ω resistors are in series so could be replaced with a 12Ω resistor The 6Ω and 3Ω resistors are in parallel. They can be replaced with a single 2 Ω resistor. The 12 Ω and 2 Ω resistors are in series and could be replaced with a single 14 Ω resistor.
Example 3: The total applied voltage to the circuit in the figure is 12 V and the resistances R 1, R 2 and R 3 are 4, 3 and 6 Ω respectively. a. Determine the equivalent resistance of the circuit. R 2 and R 3 are in parallel (R P ) 1 1 1 R p = 2 Ω R p 6 3 R P and R 1 are in series R eq = 4 + 2 = 6 Ω
The total applied voltage to the circuit in the figure is 12 V and the resistances R 1, R 2 and R 3 are 4, 3 and 6 Ω respectively. (b) What is the total current? I = V/R 12V/6Ω = 2 A (c) Find the current through and the voltage across each resistor. R 1 : I = 2 A (series) so V=IR= (2 A)(4 Ω) = 8V The remaining voltage in the circuit is 12 V 8 V = 4 V which means that V2 and V 3 are 4 V since they are in parallel. I = V/R I 2 = 4V / 3Ω 1.33 A = I 3 = 4V / 6Ω =0.67 A
Example 3: The total applied voltage to the circuit in the figure is 12 V and the resistances R 1, R 2 and R 3 are 4, 3 and 6 Ω respectively. a. Determine the equivalent resistance of the circuit. b. What is the total current? c. Find the current through and the voltage across each resistor Total 1 2 3 Voltage Current Resistance