Somebody has built a cube-shaped object by using 12 identical resistors. In the figure above, each edge of the cube is a resistor with resiatance R. The cube is connected to a battery from the corners a and z so that a current I passes over the whole cube. The problem is to find the equivalent resistance Reg of the cube. If there were no symmetry, this problem would be extremely difficult. However, by using the symmetry, it is possible to find a quick solution. Convince yourself that the symmetry implies the following: Currents in branches ae, af and ag are equal to each other. • Currents in branches fr, fq gr. gp, ep and eq are all equal to each other. • Currents in branches pz, qz and rz are all equal to each other. Using these, answer the following questions. (a) Write down the currents on the following branches along the indicated directions. On branch af flowing from a to f On branch fr flowing from f to r On branch rz flowing from r to z (b) Find the potential difference between a and z (in terms of Rand I). Vaz (c) Finally, write down the equivalent resistance between points a and z (in terms of R). Reg %3D

Somebody has built a cube-shaped object by using 12 identical resistors. In the figure above, each edge of the cube is a resistor with resiatance R. The cube is connected to a battery from the corners a and z so that a current I passes over the whole cube. The problem is to find the equivalent resistance Reg of the cube. If there were no symmetry, this problem would be extremely difficult. However, by using the symmetry, it is possible to find a quick solution. Convince yourself that the symmetry implies the following: Currents in branches ae, af and ag are equal to each other. • Currents in branches fr, fq gr. gp, ep and eq are all equal to each other. • Currents in branches pz, qz and rz are all equal to each other. Using these, answer the following questions. (a) Write down the currents on the following branches along the indicated directions. On branch af flowing from a to f On branch fr flowing from f to r On branch rz flowing from r to z (b) Find the potential difference between a and z (in terms of Rand I). Vaz (c) Finally, write down the equivalent resistance between points a and z (in terms of R). Reg %3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

There is a current of 0.25 A in the circuit of Figure P23.69.a. What is the direction of the current? Explain.b. What is the value of the resistance R?c. What is the power dissipated by R?d. Make a graph of potential versus position, starting from V = 0 V in the lower left corner and proceeding clockwise.See Figure P23.9 for an example.
In q = CVs (1-e-t/RC). Prove that RC is a unit of time. Show full and detailed solution please thank you.
In the following circuit, lo = 0.171 A, I, = 0.043 A, and I2 = 0.129 A. Find the potential difference from A to B going along the following paths (show all work): a) Through the battery and the 20 Q resistor on the bottom. b) Through the resistors in the middle (40 Q and 20 Q). c) Through the 20 Q resistor on the far right. A 40 O 6V 20 Ω 20 2 20 2 MacBook Pro B.
A 60.5 m length of insulated copper wire is wound to form a solenoid of radius 2.2 cm. The copper wire has a radius of 0.51 mm. (Assume the resistivity of copper is p = 1.7 x 10-8. m.) (a) What is the resistance of the wire? Ω (b) Treating each turn of the solenoid as a circle, how many turns can be made with the wire? turns (c) How long is the resulting solenoid? m (d) What is the self-inductance of the solenoid? mH (e) If the solenoid is attached to a battery with an emf of 6.0 V and internal resistance of 350 m2, compute the time constant of the circuit. ms (f) What is the maximum current attained? A (g) How long would it take to reach 99.9% of its maximum current? ms (h) What maximum energy is stored in the inductor? mJ
Given the parallel circuit presented below IT A I2 R2 R3 12v R1 в The total power that the Power Source of 12V provides is 120 Watts. It is known that the current 13 = 3Amp and the Resistor R2=40. Calculate the value of the resistor R1.
In the accompanying figure, the rails, connecting end pieces, and rod all have a resistance per unit length of 40/cm. The rod moves to the left at v = 3 m/s. If B = 0.65 T everywhere in the region, what is the current in the circuit (a) when a = 8 cm? (b) when a = 4.5 cm? Description of Image B Hint a. When a = 8 cm, a counterclockwise mA flows in the circuit. b. When a = = 4.5 cm, 5.48 o current of 9.75 4.0 cm X = 5.48 mA flows in the circuit. X = 9.75
In the circuit below, it is known that R1 = 10 kΩ, R2 = 15 kΩ, and C = 0.4 μF, and a battery with an Emf of 20 Volts. Initially, the connector (switch) is connected for a long time until it reaches a steady state. Then the switch is disconnected/opened at t = 0. What is the current flowing in resistor 2 at t = 4 ms?
Ex
Calculate the voltage across resistor R4.
In the figure R₁ = 9.42 kQ, R₂ = 15.7 kQ, C = 0.439 µF, and the ideal battery has emf & = 18.0 V. First, the switch is closed a long time so that the steady state is reached. Then the switch is opened at time t = 0. What is the current in resistor 2 at t = 4.10 ms? Number Units R₁ R₂ C
Consider the circuit given in the figure with V =12 V, C;=1.0 µF, C;=2.0 µF, C;=3.0 µF, C,=4.0 µF. Initially, switches S, and S, are both open, and all 's capacitors are uncharged. C, (a) The switch S, is closed for a time interval sufficiently long for the capacitor to become fully charged, what will be the charge on the capacitor C,? (b) After all capacitors are charged (with the switch S, still closed) switch S, is closed. What will be the charge on the capacitor C, ? (c) How much charge passes through the switch S, when the switch S, closes ?
The figure below shows a simplified model of a cardiac defibrillator, a device used to resuscitate patients in ventricular fibrillation. R C Riorso + When the switch S is toggled to the left, the capacitor C charges through the resistor R. When the switch is toggled to the right, the capacitor discharges current through the patient's torso, modeled as the resistor Rorso allowing the heart's normal rhythm to be reestablished. HINT (a) If the capacitor is initially uncharged with C = 8.25 µF and E = 1270 V, find the value of R (in ohms) required to charge the capacitor to a voltage of 795 V in 1.20 s. 3.904*10**-6 (b) If the capacitor is then discharged across the patient's torso with Rorso = 1240 0, calculate the voltage (in V) across the capacitor after 4.50 ms. 512.06 V