Consider the network of four resistors shown in the diagram, where R1 = 2.00 ? ,

Question

Consider the network of four resistors shown in the diagram, where R1 = 2.00 ? , R2 = 5.00 ? , R3 = 1.00 ? , and R4 = 7.00 ? . The resistors are connected to a constant voltage of magnitude V. (Figure 1)

Part A

Find the equivalent resistance RA of the resistor network.

Express your answer in ohms.

Part B

Two resistors of resistance R5 = 3.00 ? and R6 = 3.00 ? are added to the network, and an additional resistor of resistance R7 = 3.00 ? is connected by a switch, as shown in the diagram..(Figure 2) Find the equivalent resistance RB of the new resistor network when the switch is open.

Find the equivalent resistance RC of the resistor network described in Part B when the switch is closed. (Figure 2)

Figure 1:

Figure 2:

Explanation / Answer

1) R1 and R2 create an equivalent resistance of
R12 = 1 /( 1/2 + 1/5)
R12 = 1.429

so the total resistance of the circuit is
R_A = R12 + R3 + R4
R_A = 1.429 + 1 + 7
R_A = 9.43

2) R1 and R6 make an equivalent resistance of
R16 = 2 + 3 = 5

R16 in parallel to R2 of 5 gives an equivalent of
R162 = 1 / (1/5 + 1/5) = 2.5

when the switch is open R7 has no affect in the circuit so that R4 and R5 are in series with R162
R_B = R162 + R4 + R5
R_B = 2.5 + 7 + 3
R_B = 12.5

3) with the switch closed R4 and R7 become parallel and create an equivalent
R47 = 1 / (1/7 + 1/3) = 2.1

so that
R_C = R162 + R3 + R47 + R5
R_C = 2.5 + 1 + 2.1 + 3
R_C = 8.6

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