Download Class 20 Kirchhoff`s Rules

Class 20 Kirchhoff’s Rules
© Kwok-Wai Ng 2014
Reminder
Test 2 on Wednesday:
Potential and potential energy
Capacitance (all)
Resistance and resistivity, Ohm’s Law
8 multiple choice questions
2 long problems
Test ends sharply at 10:50 am.
© Kwok-Wai Ng 2014
Voltage Divider
I
R1 I
R2 I
R3
V1
V2
V3
V
I
RN
VN
Current through each individual resistor is the same
VN
V1
V2
V



R N R eff
R1 R 2
R1
or V1  V 
R1  R 2  R N
Series resistors divide and share the voltage
“proportionally”. (Larger R get the bigger share)
and similar for other resistors
© Kwok-Wai Ng 2014
Electromotive Force and Internal Resistance
A real battery
r

Electromotive force (emf ) is the
maximum possible voltage the
battery can provide between its
terminal. You can think it like the
voltage of an ideal battery with no
internal resistance.
When connected externally:
A real battery

r
I
Load R
VR
I

Rr
VR  IR 
R
Rr
Voltage across the load resistance R
will drop if more current is drawn from
the battery (by making R smaller).
© Kwok-Wai Ng 2014
About Kirchhoff’s Rules
1.There are two Kirchhoff rules – Kirchhoff’s current rule (junction rule) and Kirchhoff’s voltage rule (loop rule).
2.More complex circuits cannot be broken down into parallel and series units. The two Kirchhoff’s rules allow us to solve for any circuits, no matter how complex it is (at least theoretically).
© Kwok-Wai Ng 2014
Kirchhoff’s Current Rule (Junction Rule)
Kirchhoff’s current rule is a result of conservation of charges:
At any junction, the sum of currents must equal zero.

I0
junction
Junction formed by twisting many wires together.
© Kwok-Wai Ng 2014
Kirchhoff’s Voltage Rule
Kirchhoff’s voltage rule is a result of conservation of energy:
The sum of the potential differences across all elements around any closed circuit loop must be zero. 
V  0
closed loop
Conservation of energy:
Work done by battery = Energy stored in conservative elements (e.g. capacitors) + Energy dissipated by resistive elements (e.g. resistors)
© Kwok-Wai Ng 2014
Sign of ∆V
I
+
+
+
-
-
Always, independent of current direction
Current flows from + to ‐
Plate with positive charge is +, plate with negative charge is ‐
As you go around the loop, the “travel” direction does not need to be the same as the current direction. As you are travelling from + to ‐, ∆V is negative, it you are travelling from ‐ to +, ∆V is positive. You can also reverse this convention, but signs have to be assigned consistently with the same convention.
© Kwok-Wai Ng 2014
Dependence in Kirchhoff’s Loop Equations
You can write down Kirchhoff’s voltage equations for any closed loop you have chosen. However, the Kirchhoff’s voltage equations you have written may be dependent of each other.
Example: 3
1
2
You can write Kirchhoff’s voltage equations either for loops 1 and 2, or loops 1 and 3, or loops 2 and 3, but not 1, 2, and 3 because these three equations are dependent of each other.
© Kwok-Wai Ng 2014
Strategy in using Kirchhoff’s Rules
1. Go through every junctions in the circuit. Insert current as unknown variables (unless it is given) for every branch forming the junction. You may have to assume current directions. Make use of the Kirchhoff’s Current Rule and try to use as little of variables as possible.
2. Mark down “+” and “‐” at the two ends of each component in the current path, according to the assumed current direction. 3. Write down Kirchhoff’s Voltage Rules. Choose the loops that can make the solution easier.
4. Solve the simultaneous equations for the answers.
© Kwok-Wai Ng 2014