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Resistors in Series • All the current must follow the same path. • Each component has the same current going through it • If current is disrupted through one element (e.g. the light goes out) then they all go out. Resistors in Series • All the current must follow the same path. • Each component has the same current going through it • If current is disrupted through one element (e.g. the light goes out) then they all go out. Equivalent or total or effective resistance is the one that could replace all resistors resulting in the same current. Req = R1+ R2 + R3 Adding more resistors in series increases equivalent resistance! Resistors in Parallel • Current can branch to multiple paths • Current varies through each resistor (greater resistance = smaller current). • The current flowing into a node equals the current that flows out of that node I = I1 + I2 + I3 . • The voltage drop across each resistor is the same. • Each device is independent; if one resistor goes out, the others keep working. Resistors in Parallel • Current can branch to multiple paths • Current varies through each resistor (greater resistance = smaller current). • The current flowing into a node equals the current that flows out of that node I = I1 + I2 + I3 . • The voltage drop across each resistor is the same. • Each device is independent; if one resistor goes out, the others keep working. 1 1 1 1 = + + Req R1 R2 R3 equivalent resistance is smaller than the smallest resistance. We do: Calculating Req We do: Calculating Req Req = R1 + R2 = 8 Ω + 8 Ω = 16 Ω 1 𝑅𝑒𝑞 = 1 𝑅1 + Req = 4 Ω 1 𝑅2 = 1 8Ω + 1 8Ω = 1 4Ω We do: Calculating Req We do: Calculating Req You do: Calculating Req You do: Calculating Req Calculating Current, Potential Drop, and Power Dissipated • To calculate current through a circuit, find the Req for all resistors in a circuit, then use Ohm’s Law (I = V/R) Example: What is the current through this circuit? Calculating Current, Potential Drop, and Power Dissipated • To calculate current through a circuit, find the Req for all resistors in a circuit, then use Ohm’s Law (I = V/R) Example: What is the current through this circuit? I = 60V / 10Ω = 6A Calculating Current, Potential Drop, and Power Dissipated To find potential drop across a resistor: 1. find overall current 2. Use Ohm’s Law to find voltage drop *Note: the voltage drop of EACH parallel resistor is equal to the voltage drop across the equivalent resistor Calculating Current, Potential Drop, and Power Dissipated To find potential drop across a resistor: 1. find overall current 2. Use Ohm’s Law to find voltage drop *Note: the voltage drop of EACH parallel resistor is equal to the voltage drop across the equivalent resistor Example: What is the voltage drop across each resistor? 1st: Find Req for all resistors 2nd: Find I 3rd: Calculate V = IR for each resistor, remembering to use Req for the two parallel resistors Calculating Current, Potential Drop, and Power Dissipated To find potential drop across a resistor: 1. find overall current 2. Use Ohm’s Law to find voltage drop *Note: the voltage drop of EACH parallel resistor is equal to the voltage drop across the equivalent resistor Example: What is the voltage drop across each resistor? 1st: Find Req for all resistors Req = 5Ω + 3Ω + 8Ω = 16Ω 2nd: Find I I = 24 V / 16Ω = 1.5 A 3rd: Find voltage drop across each resistor: V1 = 5Ω* 1.5A = 7.5 V V2 = V3 = 3Ω* 1.5A = 4.5 V V4 = 8Ω* 1.5A = 12 V Calculating Current, Potential Drop, and Power Dissipated To find potential drop across a resistor: 1. find overall current 2. Use Ohm’s Law to find voltage drop *Note: the voltage drop of EACH parallel resistor is equal to the voltage drop across the equivalent resistor Example: What is the voltage drop across each resistor? Check your work! The sum of all voltage drops should equal the emf. 7.5V + 4.5V + 12V = 12V 3rd: Find voltage drop across each resistor: V1 = 5Ω* 1.5A = 7.5 V V2 = V3 = 3Ω* 1.5A = 4.5 V V4 = 8Ω* 1.5A = 12 V Calculating Current, Potential Drop, and Power Dissipated Remember that current divides up at a node. More current will go through the path with lesser resistance. To find current across parallel resistors … 1) Find the total current in a circuit 2) Find the voltage drop across the parallel resistors 3) Use Ohm’s Law Calculating Current, Potential Drop, and Power Dissipated Remember that current divides up at a node. More current will go through the path with lesser resistance. To find current across parallel resistors … 1) Find the total current in a circuit 2) Find the voltage drop across the parallel resistors 3) Use Ohm’s Law Example: What is the current across R2 and R3? 1) We already found that Itotal =1.5 amps 2) We already found that Vparallel = 3 V 3) I2 = 4.5 V / 4Ω = 1.125 A I3 = 4.5 V / 12 Ω = 0.375 A Check your work! Remember: Itotal = I2 + I3 = 1.5 amps! Calculating Current, Potential Drop, and Power Dissipated To find power dissipated across each resistor – 1) Calculate the voltage drop across each resistor 2) Calculate current through each resistor 3) Use the power law (P = IV) Example: What is the power dissipated through each resistor? 1) 2) 3) 4) P1 = IV = 1.5 A * 7.5 V = 11.25 W = 10 W P2 = IV = 1.125 A * 4.5 V = 5.06 W = 5 W P3 = IV = 0.375A * 4.5 V = 1.69 W = 2 W P4 = IV = 1.5A * 12V = 18 W = 20 W Example Example