For the circuit shown in Figure 5.56, use Ohm’s law with Kirchhoff’s current and voltage laws to determine the following: (a)The currents through each of the resistors and the voltage source. (b)The...

For the circuit shown in Figure 5.56, use Ohm’s law with Kirchhoff’s current and voltage laws to determine the following:

(a)The currents through each of the resistors and the voltage source.

(b)The equivalent resistance of all of the resistors.

1. Often systems of mass or material flow can be described using circuit analogs, because of similarities between mass flow and current. Just as electric charge can be driven in a current by potential difference, mass can be driven by differences in pressure between two points. Current flowing through resistors results in a voltage drop. Likewise, as mass flows, it also experiences a decrease in pressure as it moves through frictional (resistive) elements. A model of blood flow through systemic and pulmonary circulation is shown in Figure 5.57. Between each two components of the circulatory system (modeled as circuit elements), an approximate blood pressure is given.

(a) Derive an equation relating mass flow to pressure drop. Verify that an analog of Kirchhoff’s voltage law applies to the system shown. Based on the derivation of KVL, what can you say about the system (i.e., is the system at steady-state)?

(b) Assume that the blood flow is non-pulsatile and the volumetric flow rate is 5 L/min. What is the resistance through each component of the circulatory system? Compare the pulmonary and systemic resistances.