Phys 102
Notes 5: Basic Circuit
Analysis
This Isn’t Art Class!
Circuit Diagrams
Literal drawings are fine for
the elementary circuits, but
this would get very confusing
for larger complex ones…
Especially since most people
can’t draw that well!
So instead we use circuit
diagrams. This is a way to
convey a literal circuit in a
concise and easy to read
manner, ie. useful to other
people
Does the bulb light?
A. Yes.
B. No.
C. I’m not sure.
Even The Easy Stuff Has A lot Going On!
A Very Basic Circuit
What’s Happening?
Adding Resistance Part 1…Series
Resistors that are aligned end to end, with no junctions
between them, are referred to as “IN-SERIES.”
 The current I is the same through all resistors placed in
series.
 This is because the current has no “choice” on where to go!
 Thus the current must go through ALL of them and this
adds up!
 If we have N resistors in series, their equivalent resistance
is:
Adding Resistance Part 2…Parallel
Resistors whose left ends are held at the same potential V1, and whose right
ends are also all held at the same potential V2 are referred to as “IN-PARALLEL.”
 The potential differences V are the same across all resistors placed in parallel.
 The current can now “choose” where to go and more will go where there is less
resistance!
 You will hear the term “Path of Least Resistance” Be Careful!!!!!
 This will reduce the overall resistance of the circuit.
 If we have N resistors in parallel, their equivalent resistance is:
This Stuff From The View of Lightbulbs!
 The voltage drop across A is the same as
the total voltage drop across both B and
C.
 More current will pass through Bulb A,
and it will be brighter than either B or C.
 When the switch is closed, an alternate
pathway for the current to get from bulb
A back to the battery is created.
 This decreases the overall resistance of
the circuit, and the brightness of bulb A
increases.
What does the voltmeter read?
A.
B.
C.
D.
E.
6 V.
3 V.
2 V.
Some other value.
Nothing because
this
will fry the meter.
What does the voltmeter read?
A.
B.
C.
D.
E.
6 V.
3 V.
2 V.
Some other value.
Nothing because
this
will fry the meter.
For Series
Resistor Reduction
For Parallel
The behavior of the circuit will be unchanged if all resistors are
replaced by the single resistor Req. (AS LONG AS YOU DO IT RIGHT!!!!)
Problem 5-1
For the configuration of resistors on the
board, determine the equivalent
resistance between points a and b
Kirchhoff’s Loop Law
We have already established
that for more arbitrary paths
that for any path that starts
and ends at the same point:
What does it mean to
encounter a potential
difference????
Problem 5-2
For the circuit on the board, when the switch is open the
voltmeter reads 15V
a)Find the EMF of the battery
b)What will the current through the ammeter be when
the switch is closed?
Let’s Talk About Power Lost/Used
A current-carrying resistor dissipates power because the
electric force does work on the charges.
 The power supplied by a battery is:
 Energy and Power
 The units of power are J/s or Watts (W)
 The power dissipated by a resistor is:
 In terms of the resistance of the resistor:
QuickCheck 31.7
Which resistor dissipates more power?
A. The 9  resistor.
B. The 1  resistor.
C. They dissipate the same
power.
What Does The Wattage On A Light Bulb Refer To?
o The power rating on a bulb refers to the power dissipated in the light bulb
when plugged into a 120V potential source.
o This tells us what the resistance of the light bulb is!
o So when plugged into 120V supply separately which is brighter, a 60W or
a 100W bulb?
Very Tricky Question!
Which bulb is brighter?
A.
B.
C.
D.
The 60 W bulb.
The 100 W bulb.
Their brightnesses
are the same.
There’s not enough
information to tell.
What Happens with a Capacitor
and a Resistor?
REMEMBER THIS!!!!!
A capacitor that is initially charged yet acts as a SHORT
when connected in a circuit!
A capacitor that is fully charged acts as a BREAK when
connected in a circuit!
How does this effect out circuit analysis???
Problem 5-3
For the circuit on the board, assume the capacitors are
initially uncharged and the switch is open.
a)Immediately after the switch closes, what is the
voltage drop across each resistor?
b)After a long time has passed, what is the voltage drop
across each resistor?
Now Let’s Focus On The Time In-between!
The figure shows a charged
capacitor, a switch, and a
resistor.
At t = 0, the switch closes and
the capacitor begins to
discharge through the
resistor.
We wish to determine how
the current through the
resistor will vary as a function
of time after the switch is
closed.
Math Time!!!!
The figure shows an RC circuit, some time after the switch was closed. Using
Kirchhoff’s loop law :
The resistor current is the rate at which charge is removed from the capacitor:
Knowing that I = dQ/dt, the loop law for a simple closed RC circuit is:
Rearranging and integrating:
where the time constant  is:
Math Time – Graphically
Which capacitor discharges more
quickly after the switch is closed?
A. Capacitor A.
B. Capacitor B.
C. They discharge at
the same rate.
D. Can’t say without
knowing the initial
amount of charge.
What Does It Mean To Be GROUNDED?
If we connect one point of a circuit to
the earth by an ideal wire, we can agree
to call potential of this point to be that of
the earth: Vearth = 0 V.
The wire connecting the circuit to the
earth is not part of a complete circuit, so
there is no current in this wire! The
potential at the ground is V = 0.
 Grounding the circuit allows us to have
specific values for potential at each
point in the circuit, rather than just
potential differences.
 The circular prong of a three-prong
plug is a connection to ground.