Electrical Circuits
Lecture 29
www.physics.uoguelph.ca/~pgarrett/teaching.html
Review of L-28
• Exposure – the amount of radiation that will produce charge of either sign
in dry air at NTP
– Unit is Röntgen (R) 1 R = 2.58 × 10−4 C/kg
• Dose = amount of energy absorbed per unit mass
– SI unit Gray (Gy) = 1 J / kg
– Old unit rad = 0.01 J / kg
λeff = λ + λb =
1
2
1
2
t 12 t 1b2
Dose equivalent H = Σ wR × D
– SI unit Sievert (Sv) – Old unit rem 100 rem = 1 Sv
•
Effective decay constant
•
• For γ rays with 100 keV<Eγ< 5 MeV, µm,a ~ 3.0×10−3 m2/kg
• For photons, dose is D ≈ 3.0 × 10−3 NEt J/kg
b
• Biological half life t 1 2
t + tb
Electric potential and current
• Electric potential, or voltage V, is the potential energy that
one charge would have sitting in the electric field of all the
other charges
– Units of V are J/C → volt (V)
• Electric current, I, is the amount of charge that is moved per
unit time
– Units of I are C/s → ampere (A)
• There are many analogies between electric systems and water
systems
– Voltage is analogous to pressure
– Current is analogous to flow rate of water
– The way water flows through pipes is very similar to the way current
flow through wires
Batteries
• In water systems, pumps increase water pressure
• In electrical systems, batteries increase the voltage
High
voltage
High
pressure
pump
pH = pL+∆p
VH = VL+∆V
Low
pressure
Low
voltage
+
∆V=Vb
−
Resistance
• In water pipes, a constriction causes a pressure drop
• In electrical systems, a resistor causes a voltage drop
• Resistance measured in ohms Ω
– a 1 Ω resistor causes a 1 V drop for a current of 1 A
Low
voltage
Low
pressure
pL = pH-∆p
R
High
pressure
Direction of
electrical current
Direction of water
flow
High
voltage
Voltages
• In circuit diagrams, voltages are equal unless there is a
resistor or a battery (or some other circuit element) in place
Voltages are
the same at all
points along
the “wire”
+
−
Vb
R
decreasing
voltage
Increasing
voltage
• In real life, wires have resistance, but in diagrams, we assume
that they are zero
– can always add the equivalent resistance to the resistor
Current
• In water systems, the amount of water is conserved
– water doesn’t appear or disappear
• In electrical systems, current is conserved
current
in =
current
out
Water in
= water
out
Conservation of current
• In a closed circuit (a circuit that has no “breaks” in it), current is
conserved and any increase in voltage must match a decrease in voltage
• Define direction of current flow as you would water flow
– battery is like a water pump, so current flow in direction of increasing voltage
across the battery
Current
loop
+
−
R
Vb
decreasing
voltage
Increasing
voltage
• Ohm’s law V = IR
– Voltage drop (V) across a resistor is current (A) × resistance (Ω)
Circuit analysis
• Circuit elements that have a constant R (regardless of the values of V or I)
are ohmic
• Many circuit elements, like transistors, diodes, etc… are non-ohmic
Current
loop
+
−
R
Vb
decreasing
voltage
Increasing
voltage
• Voltage increase across battery match drop across resistor Vb = IR
• Ex. a 12 V battery is connected to a 100 kΩ resistor, what is the current?
V Vb
12 V
= 0.12 mA
I= = =
3
R R 100 × 10 Ω
Series and parallel
• Circuit elements can be in series
R1
Req = R1+R2
R2
or in parallel
R1
Is there an
equivalent resistor?
R2
Parallel circuits
R1
I1
Iin
I2
Req
Iout
R2
• From conservation of current, Iin= Iout
• Voltage drop across resistors R1 and R2 must be equal
IR
I1R1 = I2R2 = IinReq
V1 = V2
I2 = 1 1
R2
I1R1
R
= I1 1 + 1
R2
R2
R1R2
Req =
(R1 + R2 )
R1
I in Req = I1 1 +
Req = I1R1
R2
I in = I1 +
Iin = I1 + I2
Series and parallel resistors
• Resistors in series add as Req = Σi Ri
• Resistors in parallel add as
1
=
Req
1
Ri
i
• Batteries in series add as V = Σi Vi