Basic 4-Resistor, 1-Capacitor Circuit

Electricity and Magnetism Level 2

A simple RC circuit was prepared with one capacitor ( C C ) and four resistors ( R R ), as depicted in the figure shown above. All resistors have resistances of 2 Ω 2 \text{Ω} ; the capacitor's capacitance is 9 F 9 \text{F} .

Determine the time constant τ \tau in seconds.

H i n t : τ = R C Hint: \tau = R C

David's Electricity Set


The answer is 7.2.

David Hontz by David Hontz , 26, USA

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1 solution

David Hontz
Jan 10, 2017

Resistors in Series Simplication: R a = R 3 + R 4 = 2 + 2 = 4 Ω R_a = R_3 + R_4 = 2+2 = 4 \text{Ω} Resistors in Parallel Simplication: R b = ( 1 R 1 + 1 R 2 + 1 R a ) − 1 = ( 1 2 + 1 2 + 1 4 ) − 1 = 0.8 Ω R_b = \Big( \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_a} \Big) ^{-1} = \Big( \frac{1}{2} + \frac{1}{2} + \frac{1}{4} \Big) ^{-1} = 0.8 \text{Ω}

Time Constant Calculation: τ = R b C = 0.8 Ω × 9 F = 7.2 s \tau = R_bC= 0.8 \text{Ω} \times 9\text{F} = \boxed{7.2 \text{s}}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

It's pretty hard to imagine a capacitor of that capacitance!

Akshat Sharda - 3 years, 9 months ago

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