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)

Find the equivalent resistance RA of the resistor network.

Express your answer in ohms.

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.

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) For the first figure

R3 and R4 are series then R34 = 1+7 = 8

then R12 = (2*5)/(2+5) = 1.42 ohm and R34 are in series

then RA = 1.42+8 = 9.42 ohm

B) when switch is open

no effect of the inclusion of R7

then R345 = 1+7+3 = 11 ohm

R16 = 2+3 = 5 ohm

R162= 5*5/(5+5) = 2.5 ohm

RB = 2.5+11 = 13.5 ohm

C) when the switch is closed,then

R47 = (7*3)/(7+3) = 2.1 ohm

R3,R47 and R5 are in series then

R3475 = 1+2.1+3 = 6.1 ohm

R162 = 2.5 ohm

RC = 6.1+2.5= 8.6 ohm

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