Download Lesson 3 – Circuits Analysis

Circuits Analysis
SPH3U
Ms. Kueh
Recall: How do V, I, and R relate in a circuit? _________________
The most basic ways to connect loads are in series and parallel.
Series circuits offer _________________for charges to flow (charges flow from one load
to the next in series) while parallel offer charges a “choice”.
Kirchhoff’s Laws
Kirchhoff’s Current Law -
𝐼𝑜𝑢𝑡 = 𝐼𝑖𝑛 for any junction
Kirchhoff’s Voltage Law -
The sum of all voltage increases in any complete circuit
loop is equal to the sum of all voltage decreases
It’s really just conservation of energy!
𝑉𝑜𝑢𝑡 = 𝑉𝑖𝑛
These laws can be applied to determine some general rules of circuits.
Consider a series circuit with 3 resistors:
From Kirchhoff’s Voltage Law:
From Ohm’s Law:
From Kirchhoff’s Current Law:
Therefore, in a series circuit,
VT = V1 + V2 + V3
ITRT = I1R1 + I2R2 + I3R3
IT = I1 = I2 = I3
RT  R1  R2  R3  
Consider a parallel circuit with 3 resistors:
From Kirchhoff’s Current Law:
From Ohm’s Law:
From Kirchhoff’s Voltage Law:
Therefore, in a parallel circuit,
IT = I1 + I2 + I3
VT V1 V2 V3



RT R1 R2 R3
VT = V1 = V2 = V3
1
1
1
1




RT R1 R2 R3
Example 1
For the following circuit, find the values for 𝐼𝑠𝑜𝑢𝑟𝑐𝑒 , 𝐼1 ,𝐼2 ,𝐼3 , 𝑉1, 𝑉2, 𝑉3,
and 𝑅𝑡𝑜𝑡𝑎𝑙 . Where 𝑅1 = 15.0, 𝑅2 = 25.0 , 𝑅3 = 35.0 , and 𝑉 =
12.0𝑉.
V[V]
1
2
3
T
I[A]
R[Ω]
Example 2
For the following circuit 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 = 12.0 𝑉, 𝐼1 = 0.50 𝐴, 𝑉3 = 2.5 𝑉, 𝑉4 =
5.0 𝑉, and 𝑅3 = 10.0 . Find 𝐼𝑠𝑜𝑢𝑟𝑐𝑒 , 𝐼2 , 𝐼3 , 𝐼4 , 𝑉1, 𝑉2, 𝑅1 , 𝑅2 , 𝑅4 , and 𝑅𝑡𝑜𝑡𝑎𝑙 .
V[V]
1
2
3
4
T
I[A]
R[Ω]
Without calculating(!), think about how you would simplify the resistors in this diagram.