Consider the network of four resistors shown in the diagram, where R 1 = 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)

(figure 2)

Part A: Find the equivalent resistance RA of the resistor network

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.

Part C: Find the equivalent resistance RC of the resistor network described in Part B when the switch is closed.

Explanation / Answer

part a )

R1 and R2 in parallel and their equivqlen in series with R3 and R4

Req = R12 + R3 + R4

R12 = R1*R2 /R1+R2

Req = 9.4286 ohm

part b )

switch is open

so no current in R7

R1 and R6 in series and in parallel with R2

now their combination in series with R3 , R4 , R5

Req = R16 = R1 + R6

Req =[ (R1+R6)*R2 / (R1 + R2 + R6) ] + R3 + R4 + R5

Req = 13.5 ohm

part c )

now switch is closed

R4 and R7 in parallel

Req = (R16*R2 / R16 + R2 )+ R3 + R5 + (R4*R7/R4+R7)

Req = 8.6 ohm

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