DC Circuits DC Circuits

Overview Ohms Law and Power Series Circuits Parallel Circuits Series Parallel circuits

Ohm’s Law VoltageCurrentResistance Ohm’s Law is perhaps the most important law in the study of electrical circuits, since the relationship defined in the law is basic to all circuit operation. The law states the relationship between three very important electrical quantities: Voltage, Current and Resistance. The table below lists the three quantities, their units of measure, and the symbols that identify them. Ohm’s Law and Power Voltage Voltage is the electrical pressure or force which makes current flow in a circuit. Current Current is the flow of electrons through a circuit. Resistance Resistance is the opposition to current flow offered by electrical devices in a circuit.

Ohm’s Law The Current (I) in an electrical circuit is directly proportional to the Voltage (E) and inversely proportional to the Resistance. Ohm’s Law and Power Ohm’s Law simply means that the Current in an electrical circuit depends on two things: the Voltage applied to the circuit and the Resistance in the circuit.

Ohm’s Law and Power The Ohm’s Law relationships of Current, Voltage, and Resistance is expressed in three formulas: Current equals voltage divided by resistance. Resistance equals voltage divided by current. Voltage equals current multiplied by resistance. Determine the correct Formula Substitute the known Solve the Formula

Power Power Power is the amount of work performed by a circuit when voltage forces current to flow through the resistance. Thus, power is directly proportional to voltage and current. Power is measured in Watts (W). One watt of power is used when one volt causes one ampere to flow through a circuit. Ohm’s Law and Power Power equals current multiplied by voltage.

Power The Ohm's Law Wheel with Power shown below provides a graphical representation of the relationships between voltage, current, resistance and power in a direct current electrical circuit. Ohm’s Law and Power

R1 R2 R3 Ea Series Circuits Series Circuit: Series Circuit: An electronic circuit in which the power source provides Voltage to force current to flow in a single path through all the components in the circuit.

all Since all of current must go in one unbroken path through all the series resistances, the total of all the series resistors is the total resistance across the voltage source.RULE: TOTAL RESISTANCE (R t ) of the resistors in a series circuit equals the sum of the individual resistors. R t = R 1 + R 2 + R 3 Series Circuits

A Voltage Drop is the difference in potential from one side of a component to another. It is developed across each resistor depending on its resistive value.RULE: APPLIED VOLTAGE (E a ) The sum of the voltage drops of the resistors should equal the APPLIED VOLTAGE (E a ) E a = E R1 + E R2 + E R3 Series Circuit: Series Circuit: Also known as a VOLTAGE DIVIDER.

2.5 V Ea = 7.5V 7.5V R2 1kΩ R1 1kΩ R3 1kΩ Series Circuits The APPLIED VOLTAGE is divided across the resistors based on the value of the resistor. R t = 3KΩ I t = 2.5mA To calculate VOLTAGE DROP: I t R 1 = ER 1 I t R 2 = ER 2 I t R 3 = ER 3

5.35V 1.61 V.535 V Ea = 7.5V 7.5V R2 500Ω R2 500Ω R1 5kΩ R3 1.5kΩ Series Circuits To calculate VOLTAGE DROP: I t R 1 = ER 1 I t R 2 = ER 2 I t R 3 = ER 3 The APPLIED VOLTAGE is divided across the resistors based on the value of the resistor. R t = 7KΩ I t = 1.07mA

Analyze the circuit Analyze the circuit to determine whether or not the circuit is faulty. Check the Set-up and Input Check the Set-up and Input to look for obvious things that could be wrong. Calculate Values Calculate Values to determine what values that should be present. Measure Values Measure Values to determine what values that actually are present. Compare the results Compare the results to determine and verify the fault(s). Series Circuits Troubleshooting Series Circuits

There are three types of common faults: – Open – Short – Changed Value Series Circuits Series Circuits Troubleshooting Open When one resistor in a series circuit opens, the other resistors continue to operate correctly and retain their original value. The Open resistor measures Infinite Resistance and zero Current. The Voltage drop across the open component is Applied Voltage. shorted When one resistor in a series circuit shorts, the other resistors continue to operate correctly and retain their original value. The shorted resistor measures zero resistance and zero voltage drop. The circuit current increases and the voltage across the good resistors increase. change value When one resistor in a series circuit changes value, the change value component must be determined. This is accomplished by comparing the calculated and measured values

Open – Infinite R – No I – Measured Ea 7.5 V Series Circuits Series Circuits Troubleshooting

Short – Zero R – Increase total I – Voltage Drop zero 0V0V Series Circuits Troubleshooting Series Circuits

Changed Value –R increases or decreases –Measured V does not equal Calculated V 5V Series Circuits Troubleshooting Series Circuits

Parallel Circuits are circuits with two or more paths (branches) of current flow Parallel Circuits

It = Ib1 + Ib2 + Ib3 It = Ib1 + Ib2 + Ib3 R3 2kΩ R2 2kΩ R1 2kΩ b1 2mA b2 2mA b3 2mA It = 6mA Total Current (It) in a parallel circuit is the sum of the currents in the individual branches. Parallel Circuits

It = Ib1 + Ib2 + Ib3 R3 2kΩ R2 3kΩ R1 1kΩ b1 3mA b2 1mA b3 2mA It = 6mA The Resistance of each Parallel branch will affect the amount of current that will flow in that branch. Parallel Circuits

Are Current Dividers (Voltage is equal all over) Parallel Circuits

same Each branch is connected across the same Voltage source, So: Voltage is the same Potential Difference across each branch! 3.3 V Ea 3.3V Parallel Circuits TP1 TP5TP6 TP7 TP4TP3TP2 TP8

2 formulas to find TOTAL RESISTANCE (Rt): It It Va Va Rt = Rt = Ohms Law: Reciprocal: 1 Rt = Rt = Rb1 1 + Rb2 1 + Rb3 1 Parallel Circuits

Total Resistance (Rt) less Total Resistance (Rt) is always less than the value of any of the resistors in the branches of the parallel circuit. R1 1kΩ R2 3kΩ R3 2kΩ Rt = 545Ω Parallel Circuits Smallest Resistor Value

Analyze the circuit Analyze the circuit to determine whether or not the circuit is faulty. Check the Set-up and Input Check the Set-up and Input to look for obvious things that could be wrong. Calculate Values Calculate Values to determine what values that should be present. Measure Values Measure Values to determine what values are actually present. Compare the results Compare the results to determine and verify the fault(s). Parallel Circuits Troubleshooting Parallel Circuits

Parallel Circuits Troubleshooting There are three types of common faults: – Open – Short – Changed Value Parallel Circuits There is only one way to determine if there is an open resistor in a parallel circuit. The current path of the resistor must be opened and a meter inserted. Measuring the resistor value or current through the resistor will determine if the component is open. Resistance will read Infinite and current will read zero. An open component in parallel effectively removes the branch from the circuit. A shorted resistor in a parallel circuit shorts out the voltage source. To determine which resistor is shorted, you must open all the current paths in the circuit. While watching the power supply voltage, close each path or branch, one at a time. The shorted resistor shorts the power supply. The voltage reading will read zero volts, and Current will read maximum. A shorted component in a parallel circuit effectively removes other branches from the circuit. When one resistor in a Parallel circuit changes value, the change value component must be determined. This is accomplished by comparing the calculated and measured values.

Open R – Infinite R I – No I in that branch Parallel Circuits Parallel Circuits Troubleshooting

Short – Zero R – Increase total I – ALL current on shorted branch 000 Ω Parallel Circuits Parallel Circuits Troubleshooting

Changed Value –R increases or decreases –Measured I does not equal Calculated I R A Parallel Circuits Parallel Circuits Troubleshooting

Series Parallel An electronic circuit consisting of a group of Series and Parallel components in which at least one circuit element lies in the path of Total Current (It). Series-Parallel Circuits Parallel Components Series Component (It) pass through this component

To calculate for Total Resistance(Rt) in a Series-Parallel Circuit the series and parallel resistances must be simplified. R1 Series-Parallel Circuits Step 1. Equivalent Resistance (Req) Step 1. Find Total Parallel Resistance using the Reciprocal Method. This is called Equivalent Resistance (Req) Step 2. Req Step 2. Add Req to the Total Series Resistance to find Rt. Req Total Series Resistance R1 REDRAW REDRAW Circuit to simplify R1 + Req = Rt R1 + Req = Rt Req

Voltage Drops To calculate Voltage Drops in a Series-Parallel Circuit, the voltage drops in the series circuit and current in parallel circuit must be determined. ER1 EReq Series-Parallel Circuits Ea = ER1 + ER2 + EReq o The sum of the voltage drops across resistors in a series circuit equal the voltage applied across the resistors. Ea = ER1 + ER2 + EReq It = Ib1 + Ib2 o The Total Current in a parallel circuit equals the sum of all the Branch Currents It = Ib1 + Ib2 b1 ER2

Voltage Drops To calculate Voltage Drops in a Series-Parallel Circuit, the voltage drops in the series circuit and current in parallel circuit must be determined. Series-Parallel Circuits o Step 1. o Step 1. Find Rt, then use that to find It o Step 2. o Step 2. Find Voltage Drops across components connected in Series o Step 3. o Step 3. Subtract Series Voltages from Ea to find Ereq ER1 EReq b1 ER2

Series-Parallel circuits Troubleshooting ? Series-Parallel Circuits Determine a defective Series-Parallel circuit by: o Calculating the expected circuit values. o Measuring the voltage drops with a voltmeter. o Comparing the measured values with the calculated values. Use the same technique used to troubleshoot series circuits to troubleshoot the series portion of the series-parallel circuit Use the same technique used to troubleshoot parallel circuits to troubleshoot the parallel portion of the series-parallel circuit

Summary  Ohm’s Law Ohm’s Law states directly proportional inversely proportional  Ohm’s Law is one of the most significant laws in electronics, since the relationship defined in the law is basic to all circuit operation. Ohm’s Law states electric Current is directly proportional to Voltage and inversely proportional to Resistance. PowerWatts (W)  Power is the term which describes the amount of work done by an electrical circuit. Power is directly proportional to Current and Voltage. Power is measured in Watts (W).  One watt of Power is used when one Volt causes one Ampere to flow through a circuit.

Summary Series Circuit Voltage Divider  A Series Circuit is one in which the current leaves the negative terminal of the power source, flows in a single path through all components in the circuit, and enters the positive terminal of the power source. Another name for a Series Circuit is a Voltage Divider! Current  The Circuit Current is the same at any point in a series circuit. Total Current(It) can be calculated by dividing the Applied Voltage(Ea) by the Total Resistance(Rt). Voltage Drop  A Voltage Drop is the difference in potential from one side of a component to another. It is developed across each resistor depending on its resistive value. The sum of the voltage drops across all resistors in series is equal to the applied voltage. Troubleshooting  There three common faults; Opens, Shorts and Change Value Series Circuit Troubleshooting steps:  Analyze the circuit  Analyze the circuit to determine whether or not the circuit is faulty.  Check the Set-up and Input  Check the Set-up and Input to look for obvious things that could be wrong.  Calculate Values  Calculate Values to determine what values that should be present.  Measure Values  Measure Values to determine what values that actually are present.  Compare the results  Compare the results to determine and verify the fault(s).

Summary Parallel Circuit Current Divider  A Parallel Circuit is an electronic circuit that has two or more branches through which current flows. The Applied Voltage is the same across each resistor in the circuit. Another name for a Parallel circuit is a Current Divider!  All resistors in the circuit are across each other as well as across the power source. Total Current is the sum of all the branch currents in the circuit. Total ResistanceALWAYS  The reciprocal of the total Resistance is equal to the sum of the reciprocals of all of the resistors in that circuit. Total Resistance is ALWAYS smaller than the smallest branch resistance. Troubleshooting  There three common faults; Opens, Shorts and Change Value. Parallel Circuit Troubleshooting steps:  Analyze the circuit  Analyze the circuit to determine whether or not the circuit is faulty.  Check the Set-up and Input  Check the Set-up and Input to look for obvious things that could be wrong.  Calculate Values  Calculate Values to determine what values that should be present.  Measure Values  Measure Values to determine what values that actually are present.  Compare the results  Compare the results to determine and verify the fault(s).

Summary Series-Parallel  Most Circuit seen in electronics are Series-Parallel. An electronic circuit consisting of a group of Series and Parallel components in which at least one circuit element lies in the path of Total Current (It).  CurrentsVoltage drops  Currents and Voltage drops can be determined given the Applied Voltage and Resistor values in Series-Parallel circuits. Total Current can be determined by simplifying and finding the total Resistance. Voltage drops can be determined by using the Total Current. Troubleshooting a Series-Parallel Circuit  When Troubleshooting a Series-Parallel Circuit you must determine a defective Series- Parallel circuit by:  Calculating the expected circuit values.  Measuring the voltage drops with a voltmeter.  Comparing the measured values with the calculated values.