# Electric Circuits. June 12, 2013

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1 Electric Circuits June 12, 2013

2 Definitions Coulomb is the SI unit for an electric charge. The symbol is "C". Electric Current ( I ) is the flow of electrons per unit time. It is measured in coulombs per second. This measurement is also called an ampere. Therefore 1 A = 1 C/s Voltage (V) is electric potential energy per unit charge or joules/coulomb such that 1 V = 1 J/C. Named after Alessandro Volta ( ). A battery is a collection of electric cells. Each electric cell produces a flow of electron via a chemical reaction. This is the symbol for a battery. Resistance is the restriction of the flow of electrons due to the properties of the material it travels through. The symbol for resistance is "R". The unit for resistance is called the Ohm and its symbol is the Greek Omega

3 Ohm's Law Ohm's Law describes the relationship between current, voltage, and resistance. Ohm's law specifically applies to electricity traveling through metal wires. V = I R Resistors are devices used to control or reduce the electrical flow of current much like a washer can be used in a water pipe to reduce the flow of water to a shower head in order to save water. The symbol for a resistor is Various objects can be placed in the flow of electrical current to produce work. The most common are lights and motors. These items also produce a resistance much like a water wheel in a stream.

4 Electric Circuits An electric circuit is a pathway for electrical current which starts from a battery and travels back to the same battery. There are two basic types of electrical circuits, series circuits and parallel circuits. SERIES CIRCUITS In a series circuit, the resistance items are conncected one after the other in the electrical current.

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6 PARALLEL CIRCUIT In a parallel circuit, each resistance item is connected to the main flow of electrical current.

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8 Advantage & Disadvantage of Series & Parallel Circuits SERIES CIRCUIT ADVANTAGE The current or amperage does not change. Can add more batteries to increase power. DISADVANTAGE The voltage changes after each resistance item. If one item fails, the others will not work. PARALLEL CIRCUIT The voltage does not change after each resistance item. If one device fails, the others will continue to work. The amperage or current changes as it passes through each device.

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10 Calculating the Total Equivalent Resistance In a series circuit, the total equivalent resistance would be the sum of all the resistance in the circuit. R eq = R 1 + R 2 + R In a parallel circuit, the following expression is used to calculate the total equivalent resistance. R 1 = eq R R R

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12 Series Circuit ( voltage divider) R 1 R 2 R 3 R eq = R 1 + R 2 + R 3 I 1 = I 2 = I 3 V 1 = V 2 = V 3 V 1 + V 2 + V 3 = V TOTAL

13 Parallel Circuit ( current divider) R 1 R 2 R 3 I 1 = I 2 = I 3 V 1 = V 2 = V 3 I 1 + I 2 + I 3 = I TOTAL 1 = R eq R R R 1 3

14 Problem-Solving Strategies 1) Calculate R eq (Equivalent R) for the entire circuit. 2) Use Ohm's Law to find current from battery. 3) Any resisters in series with battery get I T. 4) Use V n = I T R n for resistors in series with battery. 5) Combine series /parallel rules with V = IR for each.

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16 Consider the arrangement of electrical components below. The battery supplies a total voltage of 17.9 volts. The resistors are as follows: R 1 = 7.72 Ω, R 2 = 21.9 Ω, and R 3 = 7.50 Ω. A. What is the equivalent resistance of R 2 and R 3? B. What is the equivalent resistance of the entire circuit? C. What is the total current in the circuit? D. What is the voltage drop across R 1? E. What is the voltage drop across R 2 and R 3? F. What is the current through R 1? G. What is the current through R 2? H. What is the current through R 3?

17 Consider the arrangement of electrical components below. The battery supplies a total voltage of 19.4 volts. Fill in the voltage drops and currents through each resistor in the table. Resistance values are as shown. June 12, 2013 R 1 = 9.8Ω R 2 = 9.79Ω R 3 = 6.68Ω R 4 = 8.56Ω R 5 = 9.85Ω R 6 = 7.29Ω First, find the total resistance of the entire circuit. SERIES PARALLEL R Total = R R 45 + R 6 R 123 = R 12 + R 3 R 123 = (1 / (R 1 + R 2 ) + 1 / R 3 ) -1 R 45 = (1 / R / R 5 ) -1 Then, find the total current of the circuit using Ohm's Law. Calculate the voltage drop from R 6. Now that you have the current for the entire circuit, Kirchnoff's Law says that the current in the beginning of a circuit must equal the current at the end of the circuit. Find the voltage for the parallel circuit. Since it is a parallel circuit, the voltage remains the same for both sides of the parallel circuit. Now that we have the voltage for the parallel circuit R 45, we can calculate the new current for R 4 and R 5. To find the voltage for R 3, multiply the total current by R 123. To find the current I 3... The finial two resistors are R 1 and R 2 in series which means that the voltage will change but the current will stay the same. And since this portion of the circuit is in series...

18 Consider the arrangement of electrical components below. The battery supplies a total voltage of 37.4 volts. Fill in the voltage drops and currents through each resistor in the table. Resistance values are as shown.

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