Series Circuits Analysis
From our studies of series circuits in the laboratory we found that they have several important characteristics.
Circuit Legend:
- VT is the Total Voltage
- IT is the total Current
- V1, V2, and V3 are the voltage drops across R1, R2, and R3 respectively.
- I1, I2, and I3 are the currents through R1, R2, and R3 respectively.
Series Circuits Facts:
- Voltage: The sum of all the voltage drops adds up to the total (source) voltage VT = V1 + V2 +V3
- Current: The current is always the same IT = I1 = I2 = I3
- Resistance: The Total resistance RT can be calculated in two possible ways:
- RT = R1 + R2 + R3
- RT = VT / IT (Ohm's Law)
- Power: The Total Power PT can be calculated in two possible ways:
- PT = P1 + P2 + P3
- PT = VT IT
Example:
In the circuit above, find all the unknown quantities:
GIVEN | FIND | FIND |
VTotal = VT = 100 V | IT= ? | RT= ? |
V2 = 50 V | V1 = | R 3= ? |
R2 = 5.0 Ω | V3 = | P1 = ? |
R1 = 1.0 Ω | I1 = ? | P2 = ? |
I2= 10 A | I3 = ? | PT = ? |
Solution:
(i) If I2= 10 A, Then I1 = I2 = I3 = IT = 10 A (Current is constant in a series circuit)(ii) FOR R1 V1 = I1 x R1 = 10A x 1.0 Ω = 10 V(iii) FOR V3 We know that VT = V1 + V2 +V3
Therefore 100 V = 10V + 50V + V3
V3 = 100V - 5-V - 10 V = 40V(iv) Now we can find R 3
R 3 = V 3 / I 3 = 40V / 10A = 4 Ω(v) Find the Total Resistance RT
- Method #1 ----- RT = R1 + R2 + R3 = 1.0 Ω + 5 Ω + 4 Ω = 10Ω
- Method #2 ------ RT = VT / IT (Ohm's Law)
= 100 V / 10 A = 10 Ω
You can see that both methods yield the same result(vi) Find P1 P1 = V1 x I1 = 10 V x 10 A = 100 W
This is the power used by R1(vii) Find P2 P2 = V2 x I2 = 50 V x 10 A = 500 W
This is the power used by R2(viii) Find P3 P3 = V3 x I3 = 40 V x 10 A = 400 W
This is the power used by R3(ix) Find PT PT = VT x IT = 100 V x 10 A = 1 000 W
This is the total power used by all three resistors together
Or, Alternatively, PT = P1 + P2 + P3 = 100 W + 500 W + 400 W = 1 000 W
You can see that both methods yield the same results