SERIES AND PARALLEL

SERIES

-only having one path

 for the charges

Consider Circuit A with two resistor

R1 and R2 connected in series:

By KVL 

VT = V1 + V2

Or 

 VT = IR1 + IR2

And, consider an equivalent

Circuit B with one resistor RT:

By Ohm's Law

VT = IRT

But for equivalent circuits, I is the same

for circuit A and circuit B.

   Thus 

VT = IR1 + IR2 = IRT

  Yielding 

R1 + R2 = RT

So, the equivalent total resistance for

resistor in  series is simply the

sum of the individual resistors. 

RT = R1 + R2 + R3 + . . . . . . . RN 

Also note from circuit A that:

 V2 = IR2

I = VT/RT

Thus V2 = VT(R2)/RT 

Where RT = R1 + R2

 

  

This is called the VOLTAGE DIVIDER RULE

Usually written:

VX = VT(RX)/RT

 

 PARALLEL

- from having multiple paths

for current to flow through

 so, the total equivalent resistance 

of the resistors in parallel 

connection

is:

NOTE:

I2 = V/R2

V = ITRT

Thus I2 = IT(RT)/R2

Where 1/RT = 1/R1 + 1/R2

This is called the CURRENT 

DIVIDER RULE  

Usually written:

IX = IT(RT)/RX