Triple Resistor Circuit

Electricity and Magnetism Level 1

The circuit design, shown above, consists at a 14 V 14 \text{V} battery and three resistors ( R R ). All three resistors have resistances of 6 Ω 6 \text{Ω} . Determine the current ( I I ) of the circuit in amps \text{amps} .

Hint: V = I R V=IR

David's Electricity Set


The answer is 3.5.

David Hontz by David Hontz , 26, USA

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1 solution

David Hontz
Jan 17, 2017

Resistor in Series Simplification: R a = R 2 + R 3 = 6 + 6 = 12 Ω R_a = R_2 + R_3 = 6+6 = 12 \text{Ω}

Resitor in Parallel Simplification: R b = ( 1 R 1 + 1 R a ) − 1 = ( 1 6 + 1 12 ) − 1 = ( 1 4 ) − 1 = 4 Ω R_b = \Big( \frac{1}{R_1} + \frac{1}{R_a} \Big) ^{-1} = \Big( \frac{1}{6} + \frac{1}{12} \Big) ^{-1} = \Big( \frac{1}{4} \Big) ^{-1} = 4Ω

Current Calculation: I = V R b = 14 V 4 Ω = 3.5 A I = \frac{V}{R_b} = \frac{14 \text{V}}{4 \text{Ω}} = \boxed{3.5 \text{A}}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I've done many of your problems and they're good, so I have a suggestion that you shouldn't put the formulas there as it can make problems more challenging and fun.

Akshat Sharda - 3 years, 9 months ago

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I never thought to leave out the formula before. I made sure to leave out the formulas for simplifying the circuit because I found that part the most fun, haha.

David Hontz - 3 years, 5 months ago

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