Download + 12 V

Which of the circuits shown above are wired in parallel?
1) A only
2) B only
3) C only
4) B and C
5) all of them
5A
P
8A
2A
What is the current at point P?
A)2 A
B)3 A
C)6 A
D)10 A
E) need more info to answer
Kirchhoff’s Rules (rules of thumb)
1. The SUM OF CURRENTS entering any junction
equals the sum of all currents leaving.
I1
I2
IB
I1 = I 2 + I3
I3
IA
IC
I C = IA + I B
This follows from Conservation of Charge!
When fully charged at
Q=CV=(12pF)(24v)
the circuit has
two competing
voltage steps:
+24v – 24v = 0
+
-
24 volts
R2
R3
6
12 
R1 3 
12 V
The voltage drop is
1.
2.
3.
4.
greatest across R1.
greatest across R2.
greatest across R3.
the same across each of the three resistors.
I
4
2
12 V
The current through the 2 resistor is
1. half the current through the 4.
2. the same as thru the 4.
3. twice the current through the 4.
1. ½ Ampere
3. 2 Ampere
5. 4 Ampere
2. 1 Ampere
4. 3 Ampere
6. 6 Ampere
Current in each resistor?
–IR = –8 V
I
Total resistance = 6 
–IR = – 4 V
Ohm’s Law: I = V / R
= 12 V / 6 
=2A
2
4
12 V
Start
+ = 12 V
Voltage drop across a resistor?
V=IR
V = + 12 V – 8 V – 4 V = 0 
Kirchhoff’s Rules (rules of thumb)
2. The SUM OF POTENTIAL DIFFERENCES across
all components of ANY closed circuit loop is ZERO.

R2
R1
R3
R4
 = IR1+ IR2 + IR3 + IR4
or
 - IR1 - IR2 - IR3 - IR4 = 0
This follows from Conservation of Energy!
Voltage drops enter with a – sign and
voltage gains enter with a + sign
in this equation.

I
R
+
–IR
–
+IR
Loop Rule Example
(without numbers)
The first thing we have to do is?
–I2R1
I2
I3
–I2R2
–
R1
I1
+
Define currents!
Now apply Loop rule to each loop
R2
V = +
Start
V = + I3 R3 –  = 0
R3
+ I3R3

Start
– I2R1 – I2R2 = 0
Circuits
The light bulbs in the circuit are identical. When the switch is
closed
A) both bulbs go out
B) the intensity of both bulbs increases
C) the intensity of both bulb decreases
D) nothing changes
Circuits
The light bulbs in the circuit are identical. When the switch is
closed,
a) the intensity of bulb A increases
b) the intensity of bulb A decreases
c) the intensity of bulb B increases
d) the intensity of bulb B decreases
e) nothing changes
1) A only
C)
When resistors are in parallel, the voltage drop
across each is the same.
6A
In series circuits the same current surges
3. greatest across R3. through each resistor! The voltage drop
across is IR. Same I, but different Rs!
2. the same as thru the 4.
3. 2 Ampere
D) nothing changes
e) nothing changes
See discussion on following slide
Answer
• Write a loop law for original loop:
+12V - I1R = 0
I1 = 12V/R
• Write a loop law for the new loop:
12 V
R
I
12 V
12 V
R
+12V +12V - I0R - I0R = 0
...or
I0 = 12V/R
• The key here is to determine the potential (Va–Vb)
before the switch is closed.
• From symmetry, (Va–Vb) = +12V.
• Therefore, when the switch is closed, NO additional
current will flow!
12 V
• Therefore, the current after the switch is closed is
equal to the current before the switch is closed.
12 V
R
a
I
12 V
R
b