Circuit Resistance

A 30 V 30 \text{V} battery V V is connected to a five resistor R R circuit. Each of five resistor has a resistance of 9 Ω 9 \Omega . Calculate the current I I in amperes.


David's Electricity Set


The answer is 1.25.

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3 solutions

David Hontz
Jan 2, 2017

Initial Resistors in Series Simplification: R a = R 2 + R 3 = 9 + 9 = 18 Ω R_a = R_2 + R_3 = 9+9 = 18Ω

Resistors in Parallel Simplification: R b = ( 1 R a + 1 R 4 ) 1 = ( 1 18 + 1 9 ) 1 = ( 1 6 ) 1 = 6 Ω R_b = \Big( \frac{1}{R_a} + \frac{1}{R_4}\Big)^{-1} = \Big( \frac{1}{18} + \frac{1}{9} \Big)^{-1} = \Big( \frac{1}{6} \Big)^{-1} = 6Ω

Final Resistor in Series Simplification: R c i r c u i t = R 1 + R b + R 5 = 9 + 6 + 9 = 24 Ω R_{circuit} = R_1 + R_b + R_5 = 9+6+9 = 24Ω

Current Calculation: I = V R c i r c u i t = 30 V 24 Ω = 1.25 A I = \frac{V}{R_{circuit}} = \frac{30V}{24Ω} = \boxed{1.25 A}

Sweet Problem!

James Finkelstein - 4 years, 5 months ago

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Thanks man.

David Hontz - 4 years, 5 months ago
Jose Sacramento
Jan 9, 2017

Thank you for the graphic solution.

David Hontz - 4 years, 5 months ago

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Oh.. No thanks.. Cheers

Jose Sacramento - 4 years, 4 months ago
Chew-Seong Cheong
Jan 25, 2017

Let each resistor be R = 9 Ω R=9 \Omega . The equivalent resistance connected to battery V V is given by:

R e q = R 1 + ( R 2 + R 3 ) R 4 + R 5 = R + ( R + R ) R + R = 2 R + 2 R 2 3 R = 8 3 R = 24 Ω I = V R e q = 30 24 = 5 4 = 1.25 A \begin{aligned} R_{eq} & = R_1 + (R_2+R_3) || R_4 + R_5 \\ & = R + (R+R) || R + R \\ & = 2R + \frac {2R^2}{3R} \\ & = \frac 83 R = 24 \ \Omega \\ \implies I & = \frac V{R_{eq}} = \frac {30}{24} = \frac 54 = \boxed{1.25} \text{ A} \end{aligned}

Intriguing flow. Thank you for your solution.

David Hontz - 4 years, 4 months ago

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