Chapter 10
Kirchoff's laws and circuits
1st law we have already met(sum of current in = sum of current out)
Kirchhoff's second law
in any circuit, the sum of the electromotive forces is equal to the sum of the p.d.s around a closed loop.
∑ℰ = ∑V around a closed loop
Series circuit
current is the same everywhere
e.m.f is shared around between the components
If the components have the same resistance, then e.m.f will be shared equally
if the components do not have the same resistance, the comonent with the greater proportion of resistance will take a greater proportion of e.m.f
when there are multiple surces of e.m.f, we must add the values of e.m.f, and then share between the components
if the sources are in reverse polarity we must subtract the e.m.fs
Parallel circuity
the voltage of each branch is equal to the total e.m.f of the circuit
the current is spread out over all of the branches
the higher the resistance of a branch, the lower the current that passes through it.
In complex circuits, it is useful to consider each loop seperatesly
the sum of the p.d.s of components across each branch = the total e.m.f
Examples
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Combining resistors
Resistors in series
R1= R1 + R2 + ...
resistors in parallel
1/R = 1/R1 + 1/R2 + ...
analysing circuits
example one
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lost volts is the difference in p.d. measured at the termininals of the power source than the actual em.f.
lost volts are caused by the energy that is transferred into heat and so not all the energy transferred is available for the circuit
Internal resistance is resistance which is present within a power source
ℰ = lost volts + terminal p.d.
increasing the current increases the lost volts as the increased current means that more charges travel through the cell each second so more work is done by the charges
lost volts = I x r
ℰ= V + Ir
r is the internal resistance
car batteries have a negligible internal resistance an so they can supply very large currents
ℰ= IR + Ir
ℰ=I(R+r)
V-I graphs
original graph where V = -rI + e.m.f:
double e.m.f but oringinal internal resistance:
original e.m.f but half the internal resistance:
rechargeable batteries have small internal resistance which allows them to be recharged using higher currents without overheating
high-voltage power supplies used in classrooms have very high internal resistance (often millions of ohms) acting as a safety feature preventing the power supply from delivering a fatal electric current
Investigating internal resistance
by using this circuit, we can record values for terminal p.d. for different values of current and use the variable resistor to change the resistance of the cicuit, drawing different currents from the power source
sketch the graph of e.m.f = VIr rearranged to V = -rI + e.m.f, and you will see that as the current through the cell increases, the terminal p.d. drops and the lost volts increase.
do not allow the current to high or it will raise the temperature of the cell and increase the internal resistance which we do not want in this experiment
When the current is zero the terminal p.d. is equal to the e.m.f, but as the current increases, so do the lost volts
Potential divider circuits
Potential dividers are used to divide the p.d. to give any value you require up to the total e.m.f supplied.
Ratio of resistances
V1//V2 = R1/R2
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even split of resistance means an even split of voltage