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.

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.

Express your answer in ohms.

Part C

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

Explanation / Answer

here,

A)

R1 and R2 are in parallel

their equivalent resistance , R2' = R1*R2 /( R1 + R2)

R2' = 2 * 5 /( 7)

R2' = 1.43 ohm

R2' , R3 and R4 are in series

Req = R2' + R3 + R4

Req = 9.43 ohm

B)

R1 and R6 are in series,then , R1' = R6 + R1 = 5 ohm

R1' and R2 are in parallel

their equivalent resistance , R2' = R1'*R2 /( R1' + R2)

R2' = 5 * 5 /( 10)

R2' = 2.5 ohm

R2' ,R5 , R3 and R4 are in series

Req = R2' + R3 + R4 + R5

Req = 2.5 + 1 + 7 + 3

Req = 13.5 ohm

C)

when the switch is closed

R1 and R6 are in series,then , R1' = R6 + R1 = 5 ohm

R1' and R2 are in parallel

their equivalent resistance , R2' = R1'*R2 /( R1' + R2)

R2' = 5 * 5 /( 10)

R2' = 2.5 ohm

R7 and R4 are in parallel, R4' = R4*R7/( R4 + R7)

R4' = 7 * 3 /( 10)

R4' = 2.1 ohm

R2' ,R5 , R3 and R4' are in series

Req = R2' + R3 + R4' + R5

Req = 2.5 + 1 + 2.1+ 3

Req = 8.6 ohm

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