SME
Grade 11 Science · Problem type
A series-parallel circuit
Use this for “24 V drives R₁ = 4 Ω in series with 6 Ω and 12 Ω in parallel. Find the total current, the voltage across R₁ and each branch current.”
Diagram
Rₜₒₜ = R₁ + R₂R₃/(R₂ + R₃)
Rₜₒₜ
=
4
+
6
×
12
18
=
4
+
4
=
8
Ω
I = V/Rₜₒₜ = 24/8 = 3 A
P = VI = 24 × 3 = 72 W, the three resistors’ powers added.
This is an example. Type your own values to start a new problem.
V
Battery voltage
example
R₁
Resistor 1
example
R₂
Resistor 2
example
R₃
Resistor 3
example
Rₜₒₜ
Total resistance
calculated
I
Total current
calculated
V₁
Voltage across R₁
calculated
I₂
Current in R₂
worked out (not typed)
I₃
Current in R₃
worked out (not typed)
P
Total power
calculated
Formulas
Rₜₒₜ
=
R₁
+
R₂
×
R₃
/(
R₂
+
R₃
)
8 = 4 + 6 × 12/(6 + 12)
I
=
V
/Rₜₒₜ
3
=
24
8
V₁
=
I
×
R₁
12 = 3 × 4
I₂
=
I
×
R₃
/(
R₂
+
R₃
)
2 = 3 × 12/(6 + 12)
I₃
=
I
×
R₂
/(
R₂
+
R₃
)
1 = 3 × 6/(6 + 12)
P
=
V
×
I
72 = 24 × 3
Assumptions
•
R₁ carries the whole current; then it splits between R₂ and R₃, which share one voltage.
•
Work from the inside out: the parallel pair is R₂R₃/(R₂ + R₃), then add R₁ in series.
•
The current splits between R₂ and R₃ in the opposite ratio of their resistances: the smaller one carries more.
Step-by-step
WE KNOW
V = 24 V, R₁ = 4 Ω, R₂ = 6 Ω, R₃ = 12 Ω
FIND
total resistance (Rₜₒₜ), total current (I), voltage across R₁ (V₁), current in R₂ (I₂), current in R₃ (I₃), total power (P)
Step 1 · Find total resistance (Rₜₒₜ)
Use Rₜₒₜ = R₁ + R₂ × R₃/(R₂ + R₃)
R₂
and
R₃
in
parallel,
then
R₁
in
series.
Rₜₒₜ = 4 + 6 × 12/(6 + 12)
Rₜₒₜ
=
4
+
6
×
12
18
Rₜₒₜ
=
4
+
72
18
Rₜₒₜ = 4 + 4
Rₜₒₜ = 8 Ω
Step 2 · Find total current (I)
Use I = V/Rₜₒₜ
Ohm’s law for the whole circuit: the voltage over the total resistance.
I
=
24
8
I
=
3
A
Step 3 · Find voltage across R₁ (V₁)
Use V₁ = I × R₁
All
the
current
passes
through
R₁
:
Ohm’s
law
for
R₁
.
V₁
=
3
×
4
V₁
=
12
V
Step 4 · Find current in R₂ (I₂)
Use I₂ = I × R₃/(R₂ + R₃)
The
current
divides:
R₂
takes
the
share
R₃
is
of
the
pair.
I₂
=
3
×
12/(6
+
12)
I₂
=
3
×
12
18
I₂
=
36
18
I₂
=
2
A
Step 5 · Find current in R₃ (I₃)
Use I₃ = I × R₂/(R₂ + R₃)
R₃
takes
the
share
R₂
is
of
the
pair:
the
rest
of
the
current.
I₃
=
3
×
6/(6
+
12)
I₃
=
3
×
6
18
I₃
=
18
18
I₃
=
1
A
Step 6 · Find total power (P)
Use P = V × I
The battery’s power: its voltage times the current it drives.
P
=
24
×
3
P
=
72
W
Check
Put the numbers back in. Both sides should match.
8 = 4 + 6 × 12/(6 + 12) ✓
3
=
24
8
✓
12 = 3 × 4 ✓
2 = 3 × 12/(6 + 12) ✓
1 = 3 × 6/(6 + 12) ✓
72 = 24 × 3 ✓
Topic check
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