Consider the circuit shown in the figure below. (Assume R = 6.60 and V = 19.0 V.
ID: 1397734 • Letter: C
Question
Consider the circuit shown in the figure below. (Assume R = 6.60 and V = 19.0 V.)
(a) Find the equivalent resistance of the circuit in the figure.
(b) Find each current in the circuit.
I5 = A
(c) Find the potential difference across each resistor.
(d) Find the power dissipated by each resistor.
I1 = A I2 = A I3 = A I4 = AI5 = A
(c) Find the potential difference across each resistor.
(d) Find the power dissipated by each resistor.
Pac = W Pce = W Pcd = W Ped = W Pfd = W Pdb = WExplanation / Answer
The points e and f are at the same potential. so the resistances of 9.0 Ohm (current I5) and the resistance of R=6.6 omh (current I4) are in parallel. The equivalent resistance of these two resistances is
Req1=9.0 Ohm*6.6 Ohm/(15.6 ohm)=3.81 Ohm
then Req1 and the resistance 2.4 Ohm are direct so the new Req2=Req1+2.4 Ohm=6.21 Ohm,
now the resistance Req2 is in parallel with the resistance R=6.6 Ohm (current I2)
Req3=Req2*6.6 Ohm/(Req2+6.6 Ohm)=3.2 Ohm
and finally Req3 is now in direct with the resistance 6.6 ohm located between points a and c, and the other resistance R located beween points d and b so the final equivalent resistance is
Reqf=16.4 Ohm
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The potencial delta V=I1*Reqf
I1=delta V/Reqf=1.16 Amp
I2= 0.56 Amp
I3=0.59 Amp
I4=0.34 Amp
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Delta Vac=1.16 Amp*6.6 ohm=7.64 Volts
Delta Vcd=0.56 Amp*6.6 Ohm=3.7 Volts
Delta Vdb=1.16 Amp*6.6 ohm=7.64 Volts
Delta Vce=0.59 Amp*2.4 Ohm=1.41 Volts
Delta Ved=0.34 Amp*6.6 ohm=2.24 Volts
Delta Vfd=0.25 Amp*9.0 ohm=2.25 Volts
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The power are
Pac=I1^2*6.6=8.88 W
Pce=I3^2*2.4 Ohm=0.83 W
Pcd=I2^2*6.6 Ohm=2.07 W
Ped=I4^2*6.6 Ohm=0.76 W
Pfd=I5^2*9.0Ohm=0.56 W
Pdb=8.8 W