If current is disrupted through one element (e.g. the light goes out) If current is disrupted through one element (e.g. the light goes out) then they all go out. then they all go out. Resistors in Series Each component has the same current going Each component has the same current going through it through it All the current must follow the same path. All the current must follow the same path.

Resistors in Series Each component has the same current going Each component has the same current going through it through it Adding more resistors in series increases equivalent resistance!. Equivalent or total or effective resistance is the one that could replace all resistors resulting in the same current. All the current must follow the same path. All the current must follow the same path. If current is disrupted through one element (e.g. the light goes out) If current is disrupted through one element (e.g. the light goes out) then they all go out. then they all go out.

Resistors in Parallel Current can branch to multiple paths Current can branch to multiple paths Current varies through each resistor (greater resistance = smaller current).Current varies through each resistor (greater resistance = smaller current). The current flowing into a node equals the The current flowing into a node equals the current that flows out of that node current that flows out of that node I = I 1 + I 2 + I 3. I = I 1 + I 2 + I 3. The voltage drop across each resistor is the same.The voltage drop across each resistor is the same. Each device is independent; if one resistor goes out, the others keep Each device is independent; if one resistor goes out, the others keep working. working.

Resistors in Parallel Current can branch to multiple paths Current can branch to multiple paths Current varies through each resistor (greater resistance = smaller current).Current varies through each resistor (greater resistance = smaller current). The current flowing into a node equals the The current flowing into a node equals the current that flows out of that node current that flows out of that node I = I 1 + I 2 + I 3. I = I 1 + I 2 + I 3. The voltage drop across each resistor is the same.The voltage drop across each resistor is the same. Each device is independent; if one resistor goes out, the others keep Each device is independent; if one resistor goes out, the others keep working. working. equivalent resistance is smaller than the smallest resistance.

We do: Calculating R eq

R eq = R 1 + R 2 = 8 Ω + 8 Ω = 16 Ω

We do: Calculating R eq

You do: Calculating R eq

Calculating Current, Potential Drop, and Power Dissipated To calculate current through a circuit, find the R eq 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 R eq 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? 1 st : Find R eq for all resistors 2 nd : Find I 3 rd : Calculate V = IR for each resistor, remembering to use R eq 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? 1 st : Find R eq for all resistors R eq = 5Ω + 3Ω + 8Ω = 16Ω 2 nd : Find I I = 24 V / 16Ω = 1.5 A 3 rd : Find voltage drop across each resistor: V 1 = 5Ω* 1.5A = 7.5 V V 2 = V 3 = 3Ω* 1.5A = 4.5 V V 4 = 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 3 rd : Find voltage drop across each resistor: V 1 = 5Ω* 1.5A = 7.5 V V 2 = V 3 = 3Ω* 1.5A = 4.5 V V 4 = 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 Example: What is the current across R 2 and R 3 ? 1) We already found that I total =1.5 amps 2)We already found that V parallel = 3 V 3) I 2 = 4.5 V / 4Ω = A I 3 = 4.5 V / 12 Ω = A Check your work! Remember: I total = I 2 + I 3 = 1.5 amps! 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 Example: What is the power dissipated through each resistor ? 1)P 1 = IV = 1.5 A * 7.5 V = W = 10 W 2) P 2 = IV = A * 4.5 V = 5.06 W = 5 W 3)P 3 = IV = 0.375A * 4.5 V = 1.69 W = 2 W 4)P 4 = IV = 1.5A * 12V = 18 W = 20 W 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

Example