How do you calculate total resistance in a circuit where resistors are connected in parallel or in series?

If the resistors are in parallel then the total resistance is:
1/Total resistance = 1/R1 + 1/R2 +1/R3 etc..

If the resistors are in series the total resistance is :
Total resistance = R1 + R2 + R3 etc...

I wish this helps

In series: total resistance is equal to the sum of the resistance of all resistors

So basically, Rtotal = R1 + R2 + ... + Rn

In parallel: total resistance is equal to the reciprocal of the sums of the reciprocals of the resistance of the resistors

So in more understandable terms: Rtotal = 1 / (1/R1 + 1/R2 ... + 1/Rn)

If the circuit has a mix of the two, then what you basically have to do is divide and conquer.

For example: http://sub.allaboutcircuits.com/images/00084.png

To find total resistance, first find the total resistance of the R2 and R3 portion. So:

Rtotal = 1 / (1/R2 + 1/R3)

Then, treat them as one resistor (we'll call it "R4"). You can now calculate the total resistance of the circuit by using the series circuit formula:

Rtotal = R1 + R4

or

Rtotal = R1 + 1 / (1/R2 + 1/R3)

I took EE for one year before switching to physics as an undergrad.  During that brief interlude with current that went from plus to minus and all those wires in lab, I learned one very important rule in figuring the effective resistances: start with the voltage, V, at the terminals of the power source (e.g., battery, generator).  Here's why.

Rule 1: When the R's are in parallel, the voltage V is the same across each one.
Rule 2: When the R's are in series, the voltage V is across the sum of the R's.  

With that simple bit of physics (and EE), you will come up with all the R equations you've been given to memorize by the other answers.  The difference is, by learning these two rules of voltage, you'll be able to derive those equations and know how and when to use them.

EXAMPLE:  R1, R2, and R3 are in parallel, the voltage V is across each one (Rule 1).  

So i1 = V/R1, i2 = V/R2, and i3 = V/R3 are the currents going through each R.  And that means, ta da, I = i1 + i2 + i3 = V(1/R1 + 1/R2 + 1/R3) is the total current through the circuit, from - terminal to + terminal.  [Do you see where the 1/R's come from?]

Now I [1/(1/R1 + 1/R2 + 1/R3)] = V = Ir where r = ? the total, effective resistance as I is the total current and V is the voltage across that circuit.  So there you are r = 1/(1/R1 + 1/R2 + 1/R3) is the effective total resistance for a parallel circuit...as those who would have you memorize this have indicated.

EXAMPLE:  Same R's but in series, the voltage V is across the sum of R's (Rule 2).

So V = I SUM(R) and I is the total current through the circuit from terminal to terminal, which means that current goes through each of the three R's.  And r = SUM(R) = R1 + R2 + R3 for the series circuit.

You can memorize the answers given you elsewhere, or you can learn to derive the effective resistances using the V rules.  But consider this:

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o--www---www----|.............|------x
........................|__WW__|

What's the effective resistance r between the terminals x and o for this series/parallel circuit?  Hint: Start by finding the effective resistance for the parallel portion; that becomes the third R in the series.