Resistors in Series and Parallel 25/06/2018 PAG: Experiment to determine the resistance offers by combinations of fixed resistors in both series and parallel circuits. Use (and derive) equations to determine the resistances offered by different arrangements of resistors.

You will need to draw circuit diagrams for each arrangement PAG Task Measure the resistances of 3 independent fixed resistors using a simple circuit. Record them. Connect the three in series and measure total resistance – What relationship is there? Connect the three in parallel (all possible combinations) – Measure the total resistance – What can you say about the total value compared to the values of each of the resistors? State the maximum and minimum possible resistances that can be achieved using them in combination.

Key Ideas Resistors in series: Rtotal = R1 + R2 + R3 + ... E.g. Four resistors are connected in series with resistances of 15, 22, 33 & 47 Ohms respectively. What is the total resistance?

Resistors in series: Rtotal = R1 + R2 + R3 + ... 1. Use Kirchhoff's second law (the sum of the p.d’s in a closed circuit is 0). Vtotal = V1 + V2 VTotal V1 + V2

Resistors in series: Rtotal = R1 + R2 + R3 + ... Use Ohms Law: Sub V for IR IRtotal = IR1 + IR2 (IR) Total (IR)1 + (IR)2

3. Apply Kirchhoff's first Law to the resistors. (ITotal = I1 = I2) Deriving resistors in series: Rtotal = R1 + R2 + R3 + ... 3. Apply Kirchhoff's first Law to the resistors. (ITotal = I1 = I2) Therefore I is constant and can be removed. (IR) Total (IR)1 + (IR)2

Deriving resistors in series: Rtotal = R1 + R2 + R3 + ... 4. Leaving RT = R1 + R2 … (R) Total (R)1 + (R)2

Key Ideas Resistors in parallel: 1 = 1 + 1 + 1 Rtotal R1 R2 R3 1 = 1 + 1 + 1 Rtotal R1 R2 R3 The total resistance of components in parallel is always less than the smallest individual component.

Deriving Resistance in Parallel 1 = 1 + 1 + 1 Rtotal R1 R2 R3 1. Apply Kirchhoff's first law to parallel resistors I1 ITotal ITotal I2

Deriving Resistance in Parallel 1 = 1 + 1 + 1 Rtotal R1 R2 R3 2. Apply Ohms Law: Substitute I for V/R (V/R)1 (V/R)Total (V/R)Total (V/R)2

Deriving Resistance in Parallel 3. Apply Kirchhoff’s second law to the resistors Vtotal = V1 = V2 i.e. V is constant so can be cancelled out (V/R)1 (V/R)Total (V/R)Total (V/R)2

Deriving Resistance in Parallel 4. Leaving 1/RT = 1/R1 + 1/R2 … Q. Three resistors with values of 15, 22 & 33 Ohms are connected in parallel. Calculate the total resistance in the circuit. (V/R)1 (V/R)Total (V/R)Total (V/R)2

Solving simple circuits

Solving simple circuits What will the current be through each of the resistors? What will the current be through the power source? How can the voltage be the same on each branch if the current is different? R = 10Ω R = 20Ω

Solving simple circuits Current in 20Ω resistor is half of the 10Ω resistor because it is offering twice the resistance to flow. R = 10Ω R = 20Ω

Solving simple circuits In both branches the p.d is the same because although in the bottom branch more work is done by each unit of charge fewer can get through per unit time. R = 10Ω R = 20Ω

Find the current in each resistor 6V Find the current in each resistor 2V 100Ω 2V 50Ω 25Ω

Resistors in series and parallel sheet (A Mr Gamble special) OCR Textbook P.