1. 1 DC ELECTRICAL CIRCUITS COMBINATION SERIES PARALLEL CIRCUITS

2. 2 DC ELECTRICAL CIRCUITS Kirchhoff’s laws are used to analyze and solve series parallel circuits. KIRCHHOFF’S VOLTAGE LAW states; Around a closed loop the sum of the voltage drops is equal to the sum of the voltage rises, or the algebraic sum of all the voltages is zero. THIS ALSO MEANS THE SUM OF THE VOLTAGE DROPS IN A SERIES CIRCUIT MUST EQUAL THE APPLIED VOLTAGE. Kirchhoff’s laws are used to analyze and solve series parallel circuits. KIRCHHOFF’S VOLTAGE LAW states; Around a closed loop the sum of the voltage drops is equal to the sum of the voltage rises, or the algebraic sum of all the voltages is zero. THIS ALSO MEANS THE SUM OF THE VOLTAGE DROPS IN A SERIES CIRCUIT MUST EQUAL THE APPLIED VOLTAGE.

3. 3 DC ELECTRICAL CIRCUITS KIRCHHOFF’S CURRENT LAW states; In parallel circuits the sum of the branch currents must equal the total current and the current entering a circuit must equal the current leaving the same point. CURRENT IN EQUALS CURRENT OUT. KIRCHHOFF’S CURRENT LAW states; In parallel circuits the sum of the branch currents must equal the total current and the current entering a circuit must equal the current leaving the same point. CURRENT IN EQUALS CURRENT OUT.

4. 4 DC ELECTRICAL CIRCUITS In a series parallel circuit some of the rules for series circuits will apply and some of the rules for parallel circuits will apply. An important point when analyzing and solving for this type of circuit, you must subtract your voltage drops to determine the remaining voltage for the rest of the circuit. In a series parallel circuit some of the rules for series circuits will apply and some of the rules for parallel circuits will apply. An important point when analyzing and solving for this type of circuit, you must subtract your voltage drops to determine the remaining voltage for the rest of the circuit.

5. 5 DC ELECTRICAL CIRCUITS When solving a series parallel circuit start at the opposite end of the power source and solve towards the power source. Redraw the circuit as you reduce your parallel loads. When solving a series parallel circuit start at the opposite end of the power source and solve towards the power source. Redraw the circuit as you reduce your parallel loads.

6. 6 DC ELECTRICAL CIRCUITS When working with series parallel circuits you will solve for total resistance first and then total current. Total resistance formulas for parallel branches can only be applied to branches with no series loads. When working with series parallel circuits you will solve for total resistance first and then total current. Total resistance formulas for parallel branches can only be applied to branches with no series loads. ONLY R3, R4 & R5 CAN BE PUT INTO THE RECIPROCAL FORMULA, R6 IS A SERIES LOAD BETWEEN R2 & R3.

7. 7 DC ELECTRICAL CIRCUITS Here is the same circuit with another series load R7, now we would only calculate two parallel branches. Remember we start our calculations at the opposite end of the power source and work toward the power source. Here is the same circuit with another series load R7, now we would only calculate two parallel branches. Remember we start our calculations at the opposite end of the power source and work toward the power source. START HERE, SINCE WE HAVE 2 PARALLEL BRANCHES WE CAN USE THE PRODUCT OVER SUM FORMULA

8. 8 DC ELECTRICAL CIRCUITS This combination circuits is laid out vertically, we could plug in 4 resistive values into the reciprocal formula, or use the simplified formula Rt= R/N. 400/2= 200 200/2= 100 100/2= 50 50 + 50 = 100, Rt = 100 THE NEXT SLIDE SHOWS THE PROCESS. This combination circuits is laid out vertically, we could plug in 4 resistive values into the reciprocal formula, or use the simplified formula Rt= R/N. 400/2= 200 200/2= 100 100/2= 50 50 + 50 = 100, Rt = 100 THE NEXT SLIDE SHOWS THE PROCESS.

9. 9 DC ELECTRICAL CIRCUITS THE SIMPLIFIED FORMULA IS APPLIED TO THE TWO 400 OHM BRANCHES, THEN THE CIRCUIT IS REDRAWN, THE SAME FORMULA IS USED FOR THE TWO 200 OHM BRANCHES, THEN THE CIRCUIT IS REDRAWN AGAIN, THIS IS DONE UNTIL WE ARE LEFT WITH A SERIES CIRCUIT. THE RECIPROCAL FORMULA COULD BE USED HERE TOO.

10. 10 DC ELECTRICAL CIRCUITS In this circuit we can apply the same principles, you can find the total resistance of this circuit with out a calculator, the 3, 60 Ω loads reduce to 20Ω, 60/3=20Ω plus the 100Ω = 120Ω (Rt=120Ω). WHAT DOES It = ? USE OHMS LAW!

11. 11 DC ELECTRICAL CIRCUITS One thing to remember when working with these circuits is that once you calculate the total resistance (Rt), then you will be applying ohms law throughout the rest of the circuit. Remember that voltage drops (in series) must be subtracted from the total available voltage for the circuit. One thing to remember when working with these circuits is that once you calculate the total resistance (Rt), then you will be applying ohms law throughout the rest of the circuit. Remember that voltage drops (in series) must be subtracted from the total available voltage for the circuit.

12. 12 DC ELECTRICAL CIRCUITS Find the voltage drop at R1 and the current at R3.

13. 13 DC ELECTRICAL CIRCUITS 1. The equivalent series circuit is pictured below, Rt=67.11, (It = E/R) or 78/67.11= 1.16A. 2. The voltage drop at ER1 is (E=I x R) or 1.16A x 45 Ω =52.2V 3. The voltage left for the rest of the circuit is 78 -52.2=25.8V IR3 = (I=E/R) ? 1. The equivalent series circuit is pictured below, Rt=67.11, (It = E/R) or 78/67.11= 1.16A. 2. The voltage drop at ER1 is (E=I x R) or 1.16A x 45 Ω =52.2V 3. The voltage left for the rest of the circuit is 78 -52.2=25.8V IR3 = (I=E/R) ? 1.16A -52.2V 25.8V VOLTAGE STAYS THE SAME IN PARALLEL

14. 14 DC ELECTRICAL CIRCUITS Solve for Rt and It, you can do this one in your head. HINT: R3 & R4 are in parallel with R5 & R6

15. 15 DC ELECTRICAL CIRCUITS when drawing a circuit from a word problem put your series loads first and then your parallel loads after, unless instructed to do something different in the word problem. A 42 ohm resistor is in parallel with a 100, 125 and 50 ohm resistor. when 150 volts is applied to the circuit, how much current will flow thru the 50 ohm resistor? when drawing a circuit from a word problem put your series loads first and then your parallel loads after, unless instructed to do something different in the word problem. A 42 ohm resistor is in parallel with a 100, 125 and 50 ohm resistor. when 150 volts is applied to the circuit, how much current will flow thru the 50 ohm resistor?

16. 16 DC ELECTRICAL CIRCUITS YOUR CIRCUIT WILL LOOK LIKE THE ONE BELOW. FIRST SOLVE FOR Rt THEN It, FIND YOUR VOLTAGE DROP AND CONTINUE ON FROM THERE. YOUR CIRCUIT WILL LOOK LIKE THE ONE BELOW. FIRST SOLVE FOR Rt THEN It, FIND YOUR VOLTAGE DROP AND CONTINUE ON FROM THERE.