Graded problem 1 (10 pt)
ADC circuit has similarity with the cardiovascular system of a body. The battery or voltage supply in an electric circuit is analogous to the pressure from the heart, and the electric current is analogous
to the flow of blood. The resistance determines how hard it is for the electric current (blood) to flow in the DC circuit (vascular system). Large vessels like aortae have lower resistance than smaller
vessels like capillaries. In this problem, we see a simplified DC circuit model to understand the effect of a stenosis in a blood vessel.
In the DC circuit below, the 90 Q resistor represents a large blood vessel, and it branches out to two 1600 resistors, which represent small blood vessels. The voltage on the voltage supply is V-30V.
The voltage supply "pushes" an electric current out, and the current first goes through the 900 resistor, and then, splits into two paths.
R₂ = 160 0
R₁ = 900
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V = 30 V
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R₂ = 1600
(a) What is the total resistance of the two parallel resistors, R₂ and R3? (2 pt)
(b) Seeing the two parallel resistors as one resistor with the value you found in part (a), this DC circuit is equivalent to two resistors in series. What is the total resistance of the entire DC circuit? (2
pt)
(c) What is the total electric current in the entire DC circuit? (2 pt)
When there is a stenosis in a vessel, it restricts the blood flow, and the flow resistance in the vessel increases. This situation can be simulated by increasing the resistance of a resistor. Because of the
increased resistance in the vessel, the amount of blood flow reduces, assuming that the heart still pumps out the blood with the same pressure. The reduction in the blood flow depends on where the
stenosis is. We will see that the stenosis in a small vessel (part d) affects the blood flow less than in a large blood vessel (parte).
(d) The resistance of the resistor R, is doubled to 320 Q while V. R₁ and R₂ remain the same (V = 30 V, R₁ - 9002, and R₂ = 160 02). What is the total electric current in the entire DC circuit? (2 pt)
(e) The resistance of the resistor R₂ is doubled to 1800 while V. R₂ and R₁ remain the same (V-30 V, R₂ = 160 02, and Ry - 16002). What is the total electric current in the entire DC circuit? (2 pt)