In a parallel circuit: - The voltage across each branch is equal to the source voltage - The total current is the sum of the currents in each branch - The total resistance is lower than any single branch resistance and can be calculated using the reciprocal formula or product over sum method - The total power is the sum of the power dissipated in each branch

1. Differences
Between
Series
and
Parallel
Circuits

2. Series Parallel
ET = E1 + E2 + E3 +… ET = E1 = E2 = E3 = …..
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = …
PT = P1 + P2 + P3 + …

3. Voltage relationship in a Parallel Circuit
 The top of each resistor is
connected to the same
potential - + terminal of the
 DC Supply.
 The bottom of each resistor
R1 R2 R3 is connected to the same
12 24 48
24 V
potential - - Terminal of the
DC Supply.
 Each Load (or Resistor) has
the same potential applied.

4. Series Parallel
ET = E1 + E2 + E3 +… ET = E1 = E2 = E3 = …..
IT = I1 = I2 = I3 = … IT = I1 + I2 + I3 + …
RT = R1 + R2 + R3 + …
PT = P1 + P2 + P3 + …

5. Current in a Parallel Circuit
R1 R2 R3
R1 R2 R3
24 V 12 24 48
24 V 12 24 48 I1 =2A I2 =1A
I1 =2A
R1 R2 R3 R1 R2 R3
24 V 12 24 48 12 24 48
24 V
I1 =2A I2 =1A I3 =.5A I1 =2A I2 =1A I3 =.5A
IT = 3.5A

6. Circuit Current in a Parallel
3.5A 1.5A 0.5A  The Sum of the currents entering
a point is equal to the sum of
currents leaving that point:
 E.g. – 3.5A leaves the DC Power
R1 R2 R3
24 48
Supply and arrives at the first
24 V 12
I1 =2A I2 =1A I3 =.5A node (where R1 is connected); 2A
travels through R1; the remaining
1.5A travels to R2 and R3. From
the top side of the resistors, the
0.5A
current entering a point is equal to
3.5A 1.5A
the sum of the currents entering a
point.

7. Series Parallel
ET = E1 + E2 + E3 +… ET = E1 = E2 = E3 = …..
IT = I1 = I2 = I3 = … IT = I1 + I2 + I3 + …
RT = R1 + R2 + R3 + … 1/RT = 1/R1 + 1/R2 + 1/R3 +..
PT = P1 + P2 + P3 + …

8. Parallel Resistance
 Using the Ohm’s Law Formula
(R = E/I), the resistance that
R1 R2 R3 the Power Source detects is
24 V 12 24 48 equal to 6.86 Ω.
I1 =2A I2 =1A I3 =.5A
IT = 3.5A  Each resistor is called a
branch.
RT = E T/IT
RT = 24V/3.5A
RT = 6.86

9. Parallel Resistance
 Using the Reciprocal Formula,
the Total Resistance equals
R1 R2 R3
6.86Ω, the same value arrived
24 V
I1 =2A
12
I2 =1A
24 48 at by using the R = E/I
I3 =.5A
IT = 3.5A formula.
RT = E T/IT
RT = 24V/3.5A
RT = 6.86 1/RT = 1/R1 + 1/R2 + 1/R3
1/RT = 1/12 + 1/24 + 1/48
 NOTE: the total resistance of
1/RT = (4 + 2 + 1)/48 = 7/48 the circuit is always lower than
7 RT = 48
RT = 48/7 the lowest branch resistance.
RT = 6.86

10. Parallel Resistance
R1 R2 R3
 A Scientific Calculator can be
24 V
IT = 3.5A
I1 =2A
12
I2 =1A
24
I3 =.5A
48
used to solve for the total
resistance in a parallel circuit.
RT = E T/I T
RT = 24V/3.5A
RT = 6.86 Using a Calculator
(Enter)12 (R1 value)
1/x (or X )
-1
+
(Enter)24 (R2 value)
1/x
+
(Enter)48 (R3 value)
1/x
=
1/x
=
6.86

11. Parallel Resistance
R1 R2 R3
24 V
IT = 3.5A
I1 =2A
12
I2 =1A
24
I3 =.5A
48  If only two resistors are in
RT = E T/IT
parallel, the Product over the
RT = 24V/3.5A
RT = 6.86 Sum can be used.
R(1+2) = R1 x R2
R(1+2) =
R1 + R2
12 x 24
 In the example, two resistors
12 + 24
R(1+2) =
288
36
are used and the resultant
R(1+2) = 8
resistance value replaces the
two resistors.
24 V
R1
12
R2
24
R3
48
 Then, the resultant value and
IT = 3.5A
I1 =2A I2 =1A I3 =.5A
the value of R3 can be used;
RT = E T/IT
the answer still comes up as
RT = 24V/3.5A
RT = 6.86 6.86 Ω.

12. Series Parallel
ET = E1 + E2 + E3 +… ET = E1 = E2 = E3 = …..
IT = I1 = I2 = I3 = … IT = I1 + I2 + I3 + …
RT = R1 + R2 + R3 + … 1/RT = 1/R1 + 1/R2 + 1/R3 +..
PT = P1 + P2 + P3 + … PT = P1 + P2 + P3 + …..

13. Parallel Power
 The Total Power is the sum of
the power consumed in each
branch.
48W 24W 12W
R1 R2 R3
24 V 12 24 48
I1 =2A I2 =1A I3 =.5A
IT = 3.5A
RT = 6.86
PT = I T x E T PT = P 1 + P 2+ P 3
PT = 3.5A x 24V PT = 48W + 24W + 12W
PT = 84W PT = 84W