Equivalent Resistance: Consider the network of four resistors shown in the diagr

Question

Equivalent Resistance:

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.

9.43 ohms

Now for the part that I don't know where to start

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.

Express your answer in ohms.

Please Help and Thanks in advance.

Explanation / Answer

R1 and R2 are in parallel so equivalent of these two is R' then

1/R' = 1/R1 + 1/R2 = 1/2 + 1/5

R' = 1.43 ohm

now R', R3 and R4 are in series connection,.

hence, Req = R' + R3 + R4 = 1.43 + 1 + 7 =9.43 ohm

B)
When switch is open,

R1 and R6 are in series.

R' = R1 + R6 = 2 + 3 = 5 ohm

now R' and R2 are in parallel,

1/R" = 1/R' + 1/R2 = 1/5 + 1/5

R" = 2.5 ohm

now R", R3, R4 and R5 are in series.

Req= R" + R3 + R4 + R5 = 2.5 + 1 + 7 + 3 = 13.5 ohm

C) R1 and R6 are in series.

R' = R1 + R6 = 2 + 3 = 5 ohm

now R' and R2 are in parallel,

1/R" = 1/R' + 1/R2 = 1/5 + 1/5

R" = 2.5 ohm

when switch is closed then R4 and R7 are in parallel,

1/R'" = 1/R4 + 1/R7 = 1/7 + 1/3

R'" = 2.1 ohm

now R", R'", R3 and R5 are in series.

Req = R" + R'" + R3 + R5

= 2.5 +2.1 +1 + 3 = 8.6 ohm

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