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Electric circuitsPhysicsHigh schoolabout 0:51

Resistors of 2, 3, 6 Ω are connected in parallel across 9 V. Find the equivalent resistance and total current: animated lesson

A narrated, step-by-step electric circuits video lesson with captions. Final answer: R_T = 1 Ω; I = 9 A, P = 81 W.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Resistors of 2, 3, 6 Ω are connected in parallel across 9 V. Find the equivalent resistance and total current.
2. Step by step
1. $\frac{1}{R_T} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1\ \Rightarrow\ R_T = 1\ \Omega$
  Parallel: reciprocals add
2. $I = \frac{V}{R_T} = \frac{9}{1} = 9\ \text{A}$
  Total current from Ohm's law
3. $I_{1} = 4.5\ \text{A},\ I_{2} = 3\ \text{A},\ I_{3} = 1.5\ \text{A}$
  Current in each branch (same voltage)
4. $P = VI = 81\ \text{W}$
  Power delivered
3. The answer
$\text{R\_T = 1 Ω; I = 9 A, P = 81 W}$
R_T = 1 Ω; I = 9 A, P = 81 W
4. Check
- R_T ≤ every individual resistor ✓

Transcript

The problem. Here is the problem: Resistors of 2, 3, 6 Ω are connected in parallel across 9 V. Find the equivalent resistance and total current. Resistors in parallel share the same voltage; their conductances (1/R) add.

Step by step. Parallel: reciprocals add. Total current from Ohm prime s law. Current in each branch (same voltage). The branch currents add up to the total current. Power delivered.

The answer. So the answer is R T equals 1 Ω; I equals 9 A, P equals 81 W. The equivalent resistance of a parallel network is always smaller than its smallest resistor; two equal resistors in parallel give half of one.

Check. R T less than or equal to every individual resistor, which checks out.

About electric circuits

Ohm's law, electrical power and resistors in series and parallel.

Resistors of 2, 3, 6 Ω are connected in parallel across 9…