SME
Circuit Analysis I
Ohm's and Kirchhoff's laws
Use this for “A 9 V source drives a 1.5 Ω and a 3 Ω resistor in series. Find the current, each voltage drop and the power delivered.”
Diagram
V = V₁ + V₂ = 4 V + 8 V = 12 V
I
=
V
R₁ + R₂
=
12
V
2 Ω + 4 Ω
=
2
A
Drag the source or a resistor up or down to change it.
This is an example. Type your own values to start a new problem.
Rₜ (Ω)
=
R₁ (Ω)
+
R₂ (Ω)
V (V)
=
I (A)
×
Rₜ (Ω)
V₁
Voltage across R₁
calculated
V₂
Voltage across R₂
calculated
P
Power from source
calculated
Formulas
V
=
V₁
+
V₂
12 = 4 + 8
V₁
=
I
×
R₁
4 = 2 × 2
V₂
=
I
×
R₂
8 = 2 × 4
Rₜ
=
R₁
+
R₂
6 = 2 + 4
V
=
I
×
Rₜ
12 = 2 × 6
P
=
V
×
I
24 = 12 × 2
P
=
I
2
×
Rₜ
24
=
2
2
×
6
Assumptions
•
Two resistors in series with a DC source form one loop, so the same current I flows through each (Kirchhoff’s current law).
•
Kirchhoff’s voltage law: the voltage drops around the loop add up to the source voltage.
•
Ohm’s law holds for each resistor (V = IR, R constant); wires and the source have no resistance.
Step-by-step
WE KNOW
V = 12 V, R₁ = 2 Ω, R₂ = 4 Ω
FIND
total resistance (Rₜ), current (I), power from source (P), voltage across R₁ (V₁), voltage across R₂ (V₂)
Step 1 · Find total resistance (Rₜ)
Use Rₜ = R₁ + R₂
In series the current passes through both resistors, so their resistances add.
Rₜ
=
2
+
4
Rₜ
=
6
Ω
Step 2 · Find current (I)
Use V = I × Rₜ
Ohm’s law for the whole loop: source voltage divided by total resistance.
I
=
V
Rₜ
I
=
12
6
I
=
2
A
Step 3 · Find power from source (P)
Use P = V × I
Power delivered by the source is its voltage times the current.
P
=
12
×
2
P
=
24
W
Step 4 · Find voltage across R₁ (V₁)
Use V₁ = I × R₁
Ohm’s
law
for
R₁
:
voltage
drop
is
current
times
resistance.
V₁
=
2
×
2
V₁
=
4
V
Step 5 · Find voltage across R₂ (V₂)
Use V₂ = I × R₂
Ohm’s
law
for
R₂
:
voltage
drop
is
current
times
resistance.
V₂
=
2
×
4
V₂
=
8
V
Check
Put the numbers back in. Both sides should match.
12 = 4 + 8 ✓
4 = 2 × 2 ✓
8 = 2 × 4 ✓
6 = 2 + 4 ✓
12 = 2 × 6 ✓
24 = 12 × 2 ✓
24
=
2
2
×
6
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Two resistors in parallel
Use this for “A 6 Ω and a 3 Ω resistor are in parallel across 12 V. Find each current.”
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Use this for “R₁ = 4 Ω is in series with 6 Ω ∥ 12 Ω across 24 V. Find the total resistance and every current.”
Power absorbed or delivered
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