Total Resistance in Parallel Circuits
Calculating equivalent resistance and analyzing current in parallel networks
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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 IT = I1 + I2 + I3 + I4 +…… Then …
On Reference Table
RT - Total Resistance A.K.A. "Equivalent 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/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
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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
Ex 4) Resistors of 3.0 Ω, 6.0 Ω, 9.0 Ω
are connected in parallel.
Find combined R
1/RT =
1/3.0 Ω + 1/6.0 Ω + 1/9.0 Ω
(common denominator, 18)
= (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/RT = 1/2.0 Ω + 1/4.0 Ω
1/RT = 3.0 Ω/4.0 Ω
RT = 4.0 Ω/3.0 Ω
= 1.3 ohms
b) Find IT (Current coming out of the source)
VT = ITRT
12. V = IT(1.3 ohms)
IT = 9.0 amps
c) Find the potential drop (V) across R1 & R2
VT = V1 = V2 = 12V
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Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. Which equation gives the total resistance of resistors in parallel?
2. A 3.0 Ω and a 6.0 Ω resistor are connected in parallel. What is the equivalent resistance?
3. A 12 V source is connected to a parallel circuit whose total resistance is 2.0 Ω. What is the total current?
4. Two 10. Ω resistors are in parallel. What is the total resistance?
5. A student adds another resistor in parallel and predicts the total resistance will increase. What really happens?
Two Heating Elements in Parallel
A space heater has two heating elements, 6.0 Ω and 3.0 Ω, connected in parallel across a 12-V source (a model of the real 120-V heater).
What is the equivalent resistance of the two elements?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Which statement is always true for resistors in parallel?
C2. Substitute numerical values into a mathematical representation that can be used to determine the total power produced by the heater model on the “high” setting (both elements on). Then calculate the power.
C3. Determine the current in the 6.0-Ω heating element.
C4. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C5. Which change increases the equivalent resistance of a parallel circuit?
C6. An engineer suggests wiring the two elements in series instead of in parallel across the same 12-V source. Identify one benefit and one drawback of this design. Support your answer with a calculation.