Total Resistance in Parallel Circuits

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Parallel Circuit Practice Problems

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Total Resistance Parallel Circuit

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Deriving an Equation for Total Resistance

Since I_T = I₁ + I₂ + I₃ + I₄ +……

Then …

On Reference Table

R_T - 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.

Find common denominator and solve 

1/R_T = 5/10 Ω + 2/10 Ω + 5/10 Ω

R_T = 10/12 ohms

R_T = .83 ohms

** The more resistors
 connected in parallel
the smaller the total resistance!!!

Circuits & Total Resistance

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Why?

Every time you add a resistor in parallel,

you add another branch for current,

so you create more current.

This reduces the total R. 

Total Resistance Equation #2
for parallel circuit

Ex 4) Resistors of 3.0 Ω, 6.0 Ω, 9.0 Ω are connected in parallel.

Find combined R

1/R_T =

1/3.0 Ω + 1/6.0 Ω + 1/9.0 Ω

(common denominator, 18)

 = (6.0 + 3.0 + 2.0)/18. = 11./18.

R_T = 18./11. Ω

 = 1.6 ohms

Ex. 5)

a) Find the equivalent resistance for this parallel circuit

1/R_T  = 1/2.0 Ω + 1/4.0 Ω

1/R_T = 3.0 Ω/4.0 Ω

R_T = 4.0 Ω/3.0 Ω

= 1.3 ohms

b) Find I_T (Current coming out of the source)

V_T  = I_TR_T

12. V = I_T(1.3 ohms)

I_T = 9.0 amps

c) Find the potential drop (V) across R₁ & R₂ 

V_T = V₁ = V₂ = 12V