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**Problem 1:** The conductive tissues of the upper leg can be modeled as a 40-cm-long, 12-cm-diameter cylinder of muscle and fat. The resistivities of muscle and fat are \( \rho_m = 13 \, \Omega \, m \) and \( \rho_f = 25 \, \Omega \, m \), respectively. One person's upper leg is 82% muscle, 18% fat. What current is measured if a \( \Delta V = 1.5 \, V \) potential difference is applied between the person’s hip and knee? a) Model the muscle and fat tissues as separate segments of the cylinder connected as shown in Fig. 1. The segments have the same length \( L \) but different cross sectional areas, based on their percentages. Compute separately the resistances of the muscle and the fat tissues, \( R_m \) and \( R_f \). b) The potential difference \( \Delta V \) is the same along the muscle and the fat segments. Compute the currents \( I_m \) and \( I_f \) flowing through the two segments. According to Kirchhoff’s junction law, the total current is equal to their sum, \( I = I_1 + I_2 \). Compute \( I \). c) Now approach the same problem in a different way. Imagine that the muscle and fat tissues are mixed together, and the resistivity of the mixed tissue can be found as a weighted average of the resistivities of muscle and fat, \( \rho = 0.82 \rho_m + 0.18 \rho_f \). Compute the current flowing through the entire cylinder with such resistivity. Is it far from your answer to b)? *(Answer to part c: 2.8 mA.)* **Fig. 1 Explanation:** Figure 1 is a schematic diagram for Problem 1, depicting the model of the conductive tissues. It shows two parallel segments of a cylinder, labeled "muscle" and "fat", each with length \( L \). The muscle segment has resistance \( R_m \), indicated with a current \( I_m \) flowing through it, while the fat segment has resistance \( R_f \) with a current \( I_f \) flowing through it. The total current \( I \) is shown as the sum of these two currents, consistent with Kirchhoff's junction law.

**Problem 1:** The conductive tissues of the upper leg can be modeled as a 40-cm-long, 12-cm-diameter cylinder of muscle and fat. The resistivities of muscle and fat are \( \rho_m = 13 \, \Omega \, m \) and \( \rho_f = 25 \, \Omega \, m \), respectively. One person's upper leg is 82% muscle, 18% fat. What current is measured if a \( \Delta V = 1.5 \, V \) potential difference is applied between the person’s hip and knee? a) Model the muscle and fat tissues as separate segments of the cylinder connected as shown in Fig. 1. The segments have the same length \( L \) but different cross sectional areas, based on their percentages. Compute separately the resistances of the muscle and the fat tissues, \( R_m \) and \( R_f \). b) The potential difference \( \Delta V \) is the same along the muscle and the fat segments. Compute the currents \( I_m \) and \( I_f \) flowing through the two segments. According to Kirchhoff’s junction law, the total current is equal to their sum, \( I = I_1 + I_2 \). Compute \( I \). c) Now approach the same problem in a different way. Imagine that the muscle and fat tissues are mixed together, and the resistivity of the mixed tissue can be found as a weighted average of the resistivities of muscle and fat, \( \rho = 0.82 \rho_m + 0.18 \rho_f \). Compute the current flowing through the entire cylinder with such resistivity. Is it far from your answer to b)? *(Answer to part c: 2.8 mA.)* **Fig. 1 Explanation:** Figure 1 is a schematic diagram for Problem 1, depicting the model of the conductive tissues. It shows two parallel segments of a cylinder, labeled "muscle" and "fat", each with length \( L \). The muscle segment has resistance \( R_m \), indicated with a current \( I_m \) flowing through it, while the fat segment has resistance \( R_f \) with a current \( I_f \) flowing through it. The total current \( I \) is shown as the sum of these two currents, consistent with Kirchhoff's junction law.

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Hello, I am having trouble with this problem, I was wondering if you can help me part A, Part B, and Part C and can you label which one is which, thank you

**Problem 1:** The conductive tissues of the upper leg can be modeled as a 40-cm-long, 12-cm-diameter cylinder of muscle and fat. The resistivities of muscle and fat are \( \rho_m = 13 \, \Omega \, m \) and \( \rho_f = 25 \, \Omega \, m \), respectively. One person's upper leg is 82% muscle, 18% fat. What current is measured if a \( \Delta V = 1.5 \, V \) potential difference is applied between the person’s hip and knee? a) Model the muscle and fat tissues as separate segments of the cylinder connected as shown in Fig. 1. The segments have the same length \( L \) but different cross sectional areas, based on their percentages. Compute separately the resistances of the muscle and the fat tissues, \( R_m \) and \( R_f \). b) The potential difference \( \Delta V \) is the same along the muscle and the fat segments. Compute the currents \( I_m \) and \( I_f \) flowing through the two segments. According to Kirchhoff’s junction law, the total current is equal to their sum, \( I = I_1 + I_2 \). Compute \( I \). c) Now approach the same problem in a different way. Imagine that the muscle and fat tissues are mixed together, and the resistivity of the mixed tissue can be found as a weighted average of the resistivities of muscle and fat, \( \rho = 0.82 \rho_m + 0.18 \rho_f \). Compute the current flowing through the entire cylinder with such resistivity. Is it far from your answer to b)? *(Answer to part c: 2.8 mA.)* **Fig. 1 Explanation:** Figure 1 is a schematic diagram for Problem 1, depicting the model of the conductive tissues. It shows two parallel segments of a cylinder, labeled "muscle" and "fat", each with length \( L \). The muscle segment has resistance \( R_m \), indicated with a current \( I_m \) flowing through it, while the fat segment has resistance \( R_f \) with a current \( I_f \) flowing through it. The total current \( I \) is shown as the sum of these two currents, consistent with Kirchhoff's junction law.
Transcribed Image Text:**Problem 1:** The conductive tissues of the upper leg can be modeled as a 40-cm-long, 12-cm-diameter cylinder of muscle and fat. The resistivities of muscle and fat are \( \rho_m = 13 \, \Omega \, m \) and \( \rho_f = 25 \, \Omega \, m \), respectively. One person's upper leg is 82% muscle, 18% fat. What current is measured if a \( \Delta V = 1.5 \, V \) potential difference is applied between the person’s hip and knee? a) Model the muscle and fat tissues as separate segments of the cylinder connected as shown in Fig. 1. The segments have the same length \( L \) but different cross sectional areas, based on their percentages. Compute separately the resistances of the muscle and the fat tissues, \( R_m \) and \( R_f \). b) The potential difference \( \Delta V \) is the same along the muscle and the fat segments. Compute the currents \( I_m \) and \( I_f \) flowing through the two segments. According to Kirchhoff’s junction law, the total current is equal to their sum, \( I = I_1 + I_2 \). Compute \( I \). c) Now approach the same problem in a different way. Imagine that the muscle and fat tissues are mixed together, and the resistivity of the mixed tissue can be found as a weighted average of the resistivities of muscle and fat, \( \rho = 0.82 \rho_m + 0.18 \rho_f \). Compute the current flowing through the entire cylinder with such resistivity. Is it far from your answer to b)? *(Answer to part c: 2.8 mA.)* **Fig. 1 Explanation:** Figure 1 is a schematic diagram for Problem 1, depicting the model of the conductive tissues. It shows two parallel segments of a cylinder, labeled "muscle" and "fat", each with length \( L \). The muscle segment has resistance \( R_m \), indicated with a current \( I_m \) flowing through it, while the fat segment has resistance \( R_f \) with a current \( I_f \) flowing through it. The total current \( I \) is shown as the sum of these two currents, consistent with Kirchhoff's junction law.
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