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

Question

Part A

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.

Find the equivalent resistance RA of the resistor network.

Express 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.

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.

Explanation / Answer

a) first combine R1 and R2
1/R =1/2 + 1/5 = 5/10 + 2/10 = 7/10
so R = 10/7

this is in series with 3 and 4

so Requivalength = 10/7 + 1 + 7= 9.43 ohms

b) since open we can ignore R7

first combine R1 and R6
3+2 = 5

combine this with R2
1/5 + 1/5 = 1/R
R = 2.5 ohms

this in series with R3, R4 and R5

2.5 + 1+7+3=13.5 ohms

c) now we have to combine R4 and R7

1/7 + 1/3 = 3/21 + 7/21 = 10/21 so R = 21/10

so now when we combine we have
2.5 +1 + 21/10 + 3= 8.6 ohms

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