Sometimes, we can use symmetry considerations to find the resistance of a circuit that cannot be reduced by series or parallel combinations. A classic problem of this type is illustrated in Figure P2.16. Twelve 1- Ω resistors are arranged on the edges of a cube, and terminals a and b are connected to diagonally opposite corners of the cube. The problem is to find the resistance between the terminals. Approach the problem this way: Assume that 1 A of current enters terminal a and exits through terminal b. Then, the voltage between terminals a and b is equal to the unknown resistance. By symmetry considerations, we can find the current in each resistor. Then, using KVL, we can find the voltage between a and b. Figure P2.16 Each resistor has a value of 1 Ω .
Sometimes, we can use symmetry considerations to find the resistance of a circuit that cannot be reduced by series or parallel combinations. A classic problem of this type is illustrated in Figure P2.16. Twelve 1- Ω resistors are arranged on the edges of a cube, and terminals a and b are connected to diagonally opposite corners of the cube. The problem is to find the resistance between the terminals. Approach the problem this way: Assume that 1 A of current enters terminal a and exits through terminal b. Then, the voltage between terminals a and b is equal to the unknown resistance. By symmetry considerations, we can find the current in each resistor. Then, using KVL, we can find the voltage between a and b. Figure P2.16 Each resistor has a value of 1 Ω .
Solution Summary: The circuit is shown in Figure 1. Mark the nodes and the current directions and redraw the circuit.
Sometimes, we can use symmetry considerations to find the resistance of a circuit that cannot be reduced by series or parallel combinations. A classic problem of this type is illustrated in Figure P2.16. Twelve 1-
Ω
resistors are arranged on the edges of a cube, and terminals a and b are connected to diagonally opposite corners of the cube. The problem is to find the resistance between the terminals. Approach the problem this way: Assume that 1 A of current enters terminal a and exits through terminal b. Then, the voltage between terminals a and b is equal to the unknown resistance. By symmetry considerations, we can find the current in each resistor. Then, using KVL, we can find the voltage between a and b.
Sometimes, we can use symmetry considerations to find the resistance of a circuit thatcannot be reduced by series or parallel combinations. A classic problem of this type is illustratedin Figure P2.16. Twelve 1-Ω resistors are arranged on the edges of a cube, and terminals a andb are connected to diagonally opposite corners of the cube. The problem is to find the resistancebetween the terminals. Approach the problem this way: Assume that 1 A of current enters terminal a and exits through terminal b. Then, the voltage between terminals a and b is equal tothe unknown resistance. By symmetry considerations, we can find the current in each resistor.Then, using KVL, we can find the voltage between a and b.
Find the equivalent resistance for the infinite network shown in Figure P2.12(a). Because of its form, this network is called a semi-infinite ladder. [Hint: If another section is added to the ladder as shown in Figure P2.12(b), the equivalent resistance is the same. Thus, working from Figure P2.12(b), we can write an expression for Req in terms of Req.Then, we can solve for Req.
Connect a 1-V voltage source across the terminals of the network shown in Figure P2.1(a). Then, solve the network by the mesh-current technique to find the current through the source. Finally, divide the source voltage by the current to determine the equivalent resistance looking into the terminals. Check your answer by combining resistances in series and parallel.
Chapter 2 Solutions
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