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By Francis Chuang | Semester 1 2011

Voltage Dividers

•  Used when you have resistors in series with a voltage source.

• 

Used to find the voltage across 1 or more resistors.

Use a voltage divider: 1 =  

+

() 

What about for VR2? Just use: 2 = 

+

() 

And if we have 3 resistors in series? Just use: 3  = 

++() 

And so on…

Current Dividers

• 

Used when you have resistors in parallel with a current source.•  Used to find the current going into a branch.

If we only have 2 resistors, then use a simple version of the formula:

2() = 

+()  and 1() =

 

+() 

If you have more than 2 resistors in parallel, use this general formula:

How to find VR1 and VR2 without

working out the current?

How to find i1(t) and i2(t) without

working out the voltage?

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By Francis Chuang | Semester 1 2011

Important things for solving circuits (APPLIES TO KVL AND KCL) 

•  Resistors don’t have positive or negative terminals. 

•  We can hook them up anyway around and we won’t blow up or destroy anything. 

Tips for solving KCL problems

•  As above, resistors don’t have + or – terminals, therefore we will assume a direction for

current flowing through them. 

• 

We ignore Ix and IL and their directions. Why? Because we should look at the circuit as awhole. But we will come back to that later. 

•  When assigning current directions, ALL resistors in the circuit should have consistent current

directions. 

•  We either assign them to be all going up (see RED Arrows) or all of them going down (see

BLUE arrows).

Now, how many nodes are in this circuit? The answer is 2, 1 at the top and 1 at the bottom.

When doing analysis, we just need to write equations that allow us to cover all branches. So we

can either write an equation for the top node, or an equation for the bottom node.

Let’s write equations for the Top node demonstrating both resistor current directions.

We also make the assumption that ALL currents should be leaving the node.

Assuming currents in resistors are going up:

−

6 − 6 + 3 + 3−

2 −

3 = 0 

If we assume currents in resistors are going down:

6 − 6 + 3 + 3 +

2 +

3 = 0 

We can then see that both equations are equivalent if we rearrange them later on! The key is

to be consistent.

Now, if we assume currents in resistors going up: −  = 

2  and −  =

 

3 

If we assume currents in resistors are going down:  = 

2  and  =

 

3 

Substitute to find the answer. The key is to be consistent!!!!!

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By Francis Chuang | Semester 1 2011

Tips for solving KVL problems 

•  As said before, resistors don’t have positive or negative terminals.

•  We assume that when we write a loop equation, if we hit a resistor, the terminal that we hit will

be positive.

•  We can choose any loop direction we want.

So, if we write a KVL expression for the clockwise (RED) loop:

10 + 5 +

4 − 25 = 0 

Alternatively, if we write a KVL expression taking the counter clockwise direction (BLUE):

−

4

  + 5 + 10 + 25 = 0 

See the coloured + and – signs across each resistor. You will also notice that the 2 expressions are

actually equivalent when we combine equations later.

Now, let’s write an expression for Vx, NOTE: We need to take into account the polarity as marked

on the diagram:

If we follow the clockwise loop, we hit the negative sign for the Vx label first: −  = 10 

If we follow the counter clockwise look, we hit the positive sign of the Vx label first:  = 10 

Now, you should be pro enough to work out an equation for V1.

Substitute the equations together and profit!

+ -

- ++ -

- +