Total Resistance Parallel Circuit
Circuits & Total Resistance - St. Mary's H.S.
Deriving an Equation for Total Resistance
Since IT = I1 + I2 + I3 + I4 +……
Then …
| VT | = | V1 | + | V2 | + | V3 |
| RT | R1 | R2 | R3 |
On Reference Table
| 1 | = | 1 | + | 1 | + | 1 |
| RT | R1 | R2 | R3 |
RT - total Resistance
A.K.A.
"Equivalent Resistance"
"Combined Resistance"
"Effective Resistance"
Ex 3) Find the total resistance for 3 resistors of 2.0 ohms, 5.0 ohms and 2.0 ohms connected in parallel.
| 1 | = | 1 | + | 1 | + | 1 |
| RT | R1 | R2 | R3 |
| 1 | = | 1 | + | 1 | + | 1 |
| RT | 2.0 Ω | 5.0 Ω | 2.0 Ω |
Find common denominator and solve
1/RT = 5/10 Ω + 2/10 Ω + 5/10 Ω
1/RT = (5 + 2 + 5)/10
1/RT = 12/10
RT = 10/12 ohms
RT = .83 ohms
***The more resistors connected in parallel the smaller the total resistance!!!
Why?
Every time you add a resistor in parallel, you create
more current. This reduces the total R.
Total Resistance Equation #2 for parallel circuit
RT = VT/IT
Ex 4) Resistors of 3.0 Ω,6.0 Ω,9.0 Ω are connected in parallel. Find combined R
| 1 | = | 1 | + | 1 | + | 1 |
| RT | R1 | R2 | R3 |
1/RT =
1/3.0 Ω + 1/6.0 Ω + 1/9.0 Ω
= (6.0 + 3.0 + 2.0)/18. = 11./18.
RT = 18./11. Ω
= 1.6 ohms
Ex. 5)
a) Find the equivalent resistance for this parallel circuit
| 1 | = | 1 | + | 1 | + | 1 |
| RT | R1 | R2 | R3 |
1/RT = 1/2.0 Ω + 1/4.0 Ω
1/RT = ¾
RT = 4/3 Ω
= 1.3 ohms
b)Find IT (The current coming out of the source)
VT = ITRT
12. V = IT(1.3 ohms)
IT = 9 amps
c) Find the potential drop (V) across R1 & R2
VT = V1 = V2 = V3
VT = V1 = V2 = 12 V
