More Circuit Calculations Electricity Lesson 9

Learning Objectives To know how to calculate the total emf and the total resistance for cells connected in series. To know how to calculate the total emf and the total resistance for cells connected in parallel. To know how to include diodes in circuit calculations.

Problem Solving Strategy Sketch the circuit diagram. Calculate the total circuit resistance including internal resistance. Determine current flowing through cell. Work out the current and pd for resistors in series with the cell (same current). Work out the current through parallel resistors.

Practice Question A cell with no internal resistance and an emf of 12 V is connected in series with a 6 ohm resistor and a 4 and 8 ohm resistor in parallel. What is the current flowing through each resistor?

Answer Total circuit resistance across resistors in parallel: 1/R P = 1/R 2 + 1/R 3. 1/R P = 1/4 + 1/8 = 2/8 + 1/8 = 3/8 R P = 8/3 = 2.67 Ω R Tot = R 1 + R P = = 8.67 Ω Current flowing through cell, I 1 = V/R I 1 = 12 V/ 8.67 Ω = 1.38 A

Answer II For the 8 ohm resistor, V 1 = IR 1 V 1 = 1.38 A × 6 Ω = 8.31 V P.d across 4 Ω and 8 Ω resistors, V P = ε – V 1 = 12 – 8.31 = 3.69 V Current through 4 Ω & 8 Ω resistors: I = V/R I 2 = 3.69 V / 4 Ω = 0.92 A I 3 = 3.69 V / 8 Ω = 0.46 A  Notice that I 2 + I 3 = 1.38 A (circuit rules followed)

Cell connected in Series & Parallel

Cells Connected in Series What is the net emf is each case as some of the cells are flipped? The total internal resistance is the sum of the individual internal resistances.

Cells Connected in Parallel As identical cells are added in parallel the total emf is the same as just one of the cells. If the total current in the circuit is equal to I. The current in each branch is equal to I/n for n identical cells.

Cells Connected in Parallel If each cell has internal resistance, r, the lost p.d. in each cell is equal to Ir/n. The terminal p.d. across the cells is therefore:- V = ε –v V = ε - Ir/n

Cells Connected in Parallel The cells as a source of emf ε and internal resistance r/n. So connecting cells in parallel means the cells last longer. the internal resistance gets smaller as we add cells.

Example - Solar Panels Solar panel consists of several parallel rows of identical solar cells in series. Let’s say you had 40 rows of 20 cells with an emf of 0.45 V and internal resistance 1.0 Ω. For each row: ε = 9 V and r = 20 Ω. (sum) Overall: ε = 9 V and r = 0.5 Ω. (ε same, internal resistance = 20 Ω/40)

Diodes in Circuits You can assume that a silicon diode:- has a forward pd of 0.6 V whenever current flows through it. Has infinite resistance when the pds across it is less than 0.6 V or in the reverse direction.

Example What is the current through the resistor?

Example The p.d across the diode is 0.6 V So the p.d. Across the resistor is 0.9 V Current through resistor =V/R = 0.9 V/1500 Ω