Transcript AS_Unit1_Electricity_11_More_circuit_calculations

More Circuit Calculations
Electricity Lesson 9
Learning Objectives
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To know how to calculate the total emf and the
total resistance for cells connected in series.
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To know how to calculate the total emf and the
total resistance for cells connected in parallel.
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To know how to include diodes in circuit
calculations.
Problem Solving Strategy
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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
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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.
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What is the current
flowing through each
resistor?
Answer
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Total circuit resistance across resistors in
parallel: 1/RP = 1/R2 + 1/R3.
1/RP = 1/4 + 1/8 = 2/8 + 1/8 = 3/8
RP = 8/3 = 2.67 Ω
RTot = R1 + RP = 6 + 2.67 = 8.67 Ω
Current flowing through cell, I1 = V/R
I1 = 12 V/ 8.67 Ω = 1.38 A
Answer II
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For the 8 ohm resistor, V1 = IR1
V1= 1.38 A × 6 Ω = 8.31 V
P.d across 4 Ω and 8 Ω resistors, VP = ε – V1
= 12 – 8.31 = 3.69 V
Current through 4 Ω & 8 Ω resistors: I = V/R
I2 = 3.69 V / 4 Ω = 0.92 A
I3 = 3.69 V / 8 Ω = 0.46 A
 Notice that I2 + I3 = 1.38 A (circuit rules followed)
Cell connected in Series &
Parallel
Cells Connected in Series
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What is the net emf is
each case as some of the
cells are flipped?
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The total internal
resistance is the sum of
the individual internal
resistances.
Cells Connected in Parallel
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As identical cells are
added in parallel the total
emf is the same as just
one of the cells.
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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
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If each cell has internal
resistance, r, the lost p.d.
in each cell is equal to
Ir/n.
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The terminal p.d. across
the cells is therefore:V = ε –v
V = ε - Ir/n
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Cells Connected in Parallel
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The cells as a source of
emf ε and internal
resistance r/n.
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So connecting cells in
parallel means
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the cells last longer.
the internal resistance gets
smaller as we add cells.
Example - Solar Panels
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Solar panel consists of several parallel rows of
identical solar cells in series.
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Let’s say you had 40 rows of 20 cells with an
emf of 0.45 V and internal resistance 1.0 Ω.
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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)
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Diodes in Circuits
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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
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What is the current through the resistor?
Example
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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