Consider the network of four resistors shown in the diagram, where R 1 = 2.00 ,
ID: 1329677 • Letter: C
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)
A.)Find the equivalent resistance RA of the resistor network.
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.
C.)Find the equivalent resistance RC of the resistor network described in Part B when the switch is closed.
Explanation / Answer
R1=2 ohms,
R2=5 ohms,
R3=1 ohms
R4=7 ohms
A)
R1 and R2 are in parallel combination
R12=R1*R2/(R1+R2)
=2*5/(2+5)
=1.43 ohms
and
R12, R3, R4 are in series combination,
Rnet=R123=R12+R3+R4
=1.43+1+7
=9.43 uhms
B)
R5=R6=R7=3 ohms
when the switch is open,
R1 and R6 are in series combination
R16=R1+R6
=2+3
=5 ohms
and
R16, R2 are in parallel combination
R126=R16*R2/(R16+R2)
=5*5/(5+5)
=2.5 ohms
R126, R3, R4, R5 are in series combination
Rnet=R126+R3+R4+R5
=2.5+1+7+3
=13.5 ohms
C)
when the switch is closed,
R1 and R6 are in series combination
R16=R1+R6
=2+3
=5 ohms
and
R16, R2 are in parallel combination
R126=R16*R2/(R16+R2)
=5*5/(5+5)
=2.5 ohms
and
R7 and R4 are in parallel combination
R47=R4*R7/(R4+R7)
=7*3/(7+3)
=2.1 ohms
R126, R47, R3, R5 are in series combination,
Rnet=R126+R47+R3+R5
=2.5+2.1+1+3
=8.6 ohms