Circuit Diagrams Ignore The Orientation Of The Resistor. Is This An Oversight?

A rectangular conducting homogeneous (which means the material is the same throughout) block has dimensions 1 cm × 2 cm × 3 cm 1\text{ cm} \times2\text{ cm} \times3\text{ cm} . A voltage V V is applied between all opposite faces of the block and the corresponding currents were recorded. What is the maximum current measured in Amps if the minimum current recorded is 1 mA 1\text{ mA} ?


The answer is 0.009.

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2 solutions

Prakhar Gupta
Apr 6, 2014

We know that: R = ρ l A R=\dfrac{\rho l}{A} where R = Resistance , ρ = Specific Resistance , l = length , A = Area R=\text{Resistance}, \hspace{.25cm} \rho = \text{Specific Resistance}, \hspace{.25cm} l = \text{length}, \hspace{.25cm} A = \text{Area} .
We can rewrite the equation by multiplying I I so that both sides become: I R = ρ l I A IR=\dfrac{\rho lI}{A} From Ohm's law V = I R V=IR therefore: V = ρ l I A I = V A ρ l V=\dfrac{\rho lI}{A} \longrightarrow I=\dfrac{VA}{\rho l} For minimum current A A is minimum and length is maximum: Hence A = 2 × 1 A=2\times1 and l = 3 l=3 1 = 2 V 3 ρ 1=\dfrac{2V}{3\rho} V ρ = 3 2 \dfrac{V}{\rho}=\dfrac{3}{2} For maximum current A A is maximum and l l is minumum: Hence A = 2 × 3 A=2\times3 and l = 1 l=1 : I = 6 V ρ = 6 × 3 2 = 9 mA I=\dfrac{6V}{\rho} = 6\times\dfrac{3}{2} = 9\text{mA}

Vitor da Silva
Apr 5, 2014

Considering that R=ρL/A, The three possible resistances in the solid are 2ρ/3 , 3ρ/2 and ρ/6. The minimum current flows through the maximal resistance, and V=RI. So: V=3p/2. We can rewrite this as V/ρ = 3/2. Now we use this result at the same equation but with the minimal resistance: I=V/(ρ/6) and we will end up with I=0.009 but we need to remember that this value is in miliamperes and multiply by 10⁻³.

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