A 6.0 Ω resistor and a 3.0 Ω resistor sit in parallel.
You can already say something about their combined resistance. First, check it:
A second buzzer is wired in parallel with the first. What happens to the total current from the source?
More total current at the same voltage means the pair's combined resistance is LESS than either resistor alone — less than 3.0 Ω. But how much less? This lesson's equation gives the exact value.
Read the equation carefully. It adds reciprocals — one over each resistance — not the resistances themselves.
The routine has three steps. Take the reciprocal of each branch. Add them. Then take the reciprocal of the total to find R.
Find the combined resistance of a 12 Ω resistor and a 4.0 Ω resistor in parallel.
Write down the values in the question:
R₁ = 12 Ω
R₂ = 4.0 Ω
R = ?
Write down the equation:
1/R = 1/R₁ + 1/R₂
Substitute in the values:
1/R = 1/12 + 1/4.0
Simplify:
1/R = 0.333
Find R — take the reciprocal of both sides:
R = 3.0 Ω
Check: 3.0 Ω is smaller than both 12 Ω and 4.0 Ω.
Always run that last check: the combined resistance of a parallel pair must be smaller than either branch. The check also guards the classic slip of stopping too early — 1/R = 0.333 is not the answer. R is.
For 10 Ω and 15 Ω in parallel, a student's answer is 12.5 Ω. Which check shows it must be wrong?
For 12 Ω and 6.0 Ω in parallel, a student answers 0.25 Ω. Which step did the student miss?
Find the combined resistance of 10 Ω and 40 Ω in parallel, in Ω.
A 20 Ω resistor and a 5.0 Ω resistor sit in parallel. Calculate their combined resistance, in Ω.
An 18 Ω resistor and a 9.0 Ω resistor sit in parallel. Calculate their combined resistance, in Ω.