Series and Parallel Circuits | Toronto Metropolitan University

University:
Toronto Metropolitan University
Course:
LAW 122 | Business Law
Academic year:

2024
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3
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Series and Parallel Circuits Series Circuit Rules A “Series Circuit” follows a single loop or path Parallel Circuit Rules A “Parallel Circuit” follows a multi loop or path Voltage Gain = Sum of V1 +V2+V3 Current = IT = I1 = I2 = I3 Equations Total Resistance = RT = R1+R2+R3 Voltage = Ohm’s Law V= I x R Voltage Gain = VT = V1 = V2 = V3 Current = IT = I1+I2+I3 Equations Total Resistance = 1/RT= 1/R1+1/R2+1/R3 Voltage = Ohm’s Law V= I x R Let’s do an Example for the following Series Circuit: 1. What is the total voltage gain in the circuit? VT = 12V 2. What is the Equivalent Resistance of the circuit? RT = R1+R2+R3 RT = 10Ω+20Ω+30Ω RT = 60Ω 3. What is the total current through the circuit? V=IxR IT = VT /RT IT= 12V/60Ω IT = 0.2A 4. What is the current through each Resistor? IT = I1 = I2 = I3 Note: there is no place to add or remove current Therefore: I1 = 0.2A I2 = 0.2A I3 = 0.2A 5. What is the Voltage drop? V1 = I1 x R1 V1 = 0.2A x 10Ω = 2V V2 = 0.2A x 20Ω = 4V V3 = 0.2A x 30Ω = 6V VT = V1+V2+V3 VT = 2V+4V+6V VT = 12V Let’s do an Example for the following Parallel Circuit: 6. What is the total voltage gain in the circuit? VT = 20V 7. What is the Equivalent Resistance of the circuit? 1/RT = 1/R1+1/R2+1/R3 1/RT = 1/7Ω+1/15Ω+1/12Ω 1/RT = 0.293 RT = 1/ 0.293Ω RT = 3.41Ω 8. What is the total current through the circuit? V = I x R = you need to divide each side by R IT = VT /RT IT= 20V/3.41Ω IT = 5.87A 9. What is the Voltage drop? VT = V1 = V2 = V3 V1 = 20V V2 = 20V V3 = 20V 10. What is the current through each Resistor? IT = I1 + I2 + I3 I1 = V1/R1 I1 = 20V/7Ω I1 = 2.86A I2 = V2/R2 I2 = 20v/15Ω I2 = 1.34A IT = 2.86A + 1.34A + 1.67A IT = 5.87A I3 = V3/R3 I3 = 20v/12Ω I3 = 1.67A 20V 7Ω 15Ω 12Ω Combination Circuit Example: 8Ω 12Ω 24V 1. What is the total voltage gain in the circuit? VT = 24V 2. What is the Equivalent Resistance of the circuit? 1/R1, R2 = 1/R1 +1/ R2 1/R1, R2 = 1/12Ω + 1/5Ω 1/R1, R2 = 1/0.283 R1, R2 = 3.53Ω RT = 3.53Ω + 8Ω RT = 11.53Ω 3. What is the total current through the circuit? V=IxR IT = VT /RT IT= 24V/11.53Ω IT = 2.08A 4. What is the current through each Resistor? I3 = IT = 2.08A I1 = V1/R1 I2 = V2/R2 I1 = 7.36V/12Ω I2 = 7.36/5Ω I1 = 0.61A I2 = 1.47A I1 + I2 = 0.61A + 1.47A = 2.08A 5. What is the Voltage drop? NOTE THIS QUESTION NEEDS TO BE DONE PRIOR TO Q#4 V3 = I3xR3 V3 = 2.08A x 8Ω V3 = 16.64V V1, 2 = I1, 2 x R1, 2 V1, 2 = 2.08A x 3.53Ω V1, 2 = 7.34V V1, 2 = VT –V3 V1, 2 = 24V – 16.64V V1, 2 = 7.36V