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DC electric circuits
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Electric circuits
Electric current
Charge can move freely in a conductor if an electric field is present; the moving charge is an electric
current (SI unit is the ampere (A), often shortened to amps).
• We use the potential difference or voltage across the conductor to characterize the electric field
(since ∆V = E∆x)
• The current that flows is determined by the potential difference across the conductor and the
resistance of the conductor (Ohm’s law):
V = IR
The SI unit of resistance is the ohm (Ω).
As current flows through a resistance, energy is lost:
P = VI
If the current is constant (which also means it doesn’t change direction), the current is called a direct
current or DC.
What is an electric circuit?
To maintain a steady electric current, the moving charge needs to be able to return to its starting
location – a complete circuit must be present.
Since energy lost as the charge moves, this energy must be replaced by a power supply. The main ways
to produce an electric current are generators using electromagnetic induction, and chemical batteries.
The exact type of power supply is not important, how much energy is supplied is. We measure this
energy by the potential difference provided by the power supply – also called the voltage of the
power supply.
Note that the potential difference across a resistance is a potential drop, or a reduction in energy. The
potential difference across a power supply is a potential rise – a gain in energy.
For a steady current, if we go around a complete circuit, the total energy supplied is equal to the total
energy lost:
∑ Vsupply = ∑ Vlosses
Usually, a simple circuit will only contain a single power supply. If we make all potential rises
positive, and all potential drops negative, we can write:
∑V = 0
around any closed circuit.
DC electric circuits
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Circuit diagrams
An easy way to describe an electric circuit is with a circuit diagram – a drawing showing the circuit.
Standard symbols are used for the various components in the circuit, and the conductors (wires)
joining them together are drawn as lines.
Circuit symbols: power supply
A DC power supply can be drawn in a number of different ways (we’ll use the one on the left):
+9 V
+
9V
−
Resistors
If the resistance of a component of an electric circuit is its main electrical property, we can call it a
resistor.
Why do we want to add resistance to a circuit?
• A component might perform some useful function, but its main electrical property is resistance
– we can represent it with a resistor. (For example, a heating element, or a light bulb.)
• We can use a resistor to control the current in a circuit. Once we put a resistor in a circuit, its
resistance is so much larger than the resistance of the wires in the circuit, and we can assume
that the resistance of the wires is zero.
Circuit symbols: resistor
Example: a 1.0 kΩ resistor connected to a 12 V power supply:
12 V
1.0 kΩ
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Series & parallel circuits
Multiple components in a circuit can either be connected
• in series with each other
R1
R2
R3
• in parallel with each other
R1
R2
R3
Series circuits
Example: a 1.0 kΩ and a 2.0 kΩ resistor connected in series with a 12 V power supply:
1.0 kΩ
12 V
2.0 kΩ
Note that
• as the current flows from A to B, power is lost in each resistor, so
VAB = V1 + V2
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• the same current flows through all the resistors
IA = I1 = I2 = IB
• the combined resistance of both resistors is
RT = R1 + R2
Example: a 1.0 kΩ and a 2.0 kΩ resistor connected in parallel with a 12 V power supply:
12 V
1.0 kΩ
2.0 kΩ
Note that
• all the resistors connect the same two points in the circuit together, so they must all have the
same potential difference across them
VAB = V1 = V2
• the current at A splits up to flow through all of the resistors
IA = I1 + I2 = IB
• the combined resistance of both resistors is
1
1
1
=
+
RT
R1
R2
Measuring currents and voltages
We use ammeters and voltmeters to measure current and potential difference.
ammeter
The current to be measured must flow through the meter – connect in series
A
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voltmeter
We want to measure the potential difference across two points – connect in parallel across these two
points
V
A
B
A multimeter is a convenient device that can measure either voltage or current (and resistance as
well).
Capacitors ADVANCED
Two parallel plates with positive and negative charges equal in magnitude can be used to store electrical energy. This is called a capacitor. This energy can be used as a power supply in a circuit. The
stored energy depends on the charge and the capacitance (measured in farads (F)).
Q = CV
Since the potential difference between the two plates depends on the charge on the plates, the voltage
across the capacitor will fall as current flows from it – as the capacitor discharges.
How quickly the voltage falls depends on how much current flows, which depends on the resistance
in the circuit.
V = V0 exp −t/ RC
where R is the resistance in the circuit and C is the capacitance of the capacitor. The quantity RC is
called the time constant, and is usually written as τ .
Similarly, it takes time to charge a capacitor:
V = V0 (1 − exp −t/τ )
This can be used to measure time in DC circuits.
When the capacitor is fully charged or discharged, no current will flow.
Circuit symbols: capacitor
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AC circuits EXTRA
Another common type of electric current is alternating current, or AC.
In an AC circuit, the current varies sinusoidally, and flows first in one direction, and then the other.
If a suitable average voltage and current are used for AC, Ohm’s Law can still be used for circuits
which only contain resistors.