Consider the following. (a) A rectangular block has the dimensions ? ? w ? h . W

Question

Consider the following.

(a) A rectangular block has the dimensions ? ? w ? h. When a battery with a voltage V is connected across the end faces as shown in the left figure above, a current I1 flows through the circuit. If the same battery is connected across the top and bottom faces of the block as shown in the right figure, what is the current I2 that flows through the circuit? Give your answer in terms of I1. (Use the following as necessary: ?, w, h, I1)
I2 =   

(b) Suppose ? = 3.80 cm, w = 2.2 cm, and h = 1.00 cm; the battery voltage is 1.5 V and I1 = 3.30 A, determine the value of I2.

Explanation / Answer

R = V/I

thus, R1 = V/I1 = 1.5/3.30 ohm = 5/11 ohm

R1 = rho * length/area = rho * L/(w*h) (written L for no confussion)

=> 5/11 = rho * 3.80/(2.2 * 1.00)

=> rho = 1.73

therefore, R2 = rho * h/(L*w)

R2 = 1.73* 1.0/(3.80 * 2.2)

R2 = 0.21 ohms

thus I2 =V/R2 = 1.5/0.21 = 7.14 A

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