a) What is the equivalent resistance of the four resistors? In other words, what

Question

a) What is the equivalent resistance of the four resistors? In other words, what single resistor would replace all four resistors and still draw the same current from the battery?  

b) What is the current directly out of the battery?  A

c) The voltage across the three resistors with 10 , 48 , and 16 must be the same.  ---Select--- False True

d) Use the information above to find and tabulate the current through and the potential difference across each resistor.

resistor current (A) potential difference (V) 3 R (10 ) 48 16

Explanation / Answer

let,

R1=3ohms, R2=10 ohms, R3=48 ohms, R4=16 ohms

v=12 v

a)

R2, R3 and R4 are in parallel combination,

1/R234 = 1/R2 + 1/R3 + 1/R4

1/R234= 1/10 + 1/48 + 1/16

===> R234=5.45 ohms

Rnet = R1+ R234

=3+5.45

=8.45 ohms

b)

current I=V/Rnet

I=12/8.45

I=1.42 A

c)

true ,

here voltge is same because R2, R3 and R4 are in parallel combination,

d)

here,

I1=I234 = 1.42 A

V1=I1*R1 = 1.42*3 = 4.26 v

and

V234 = I234*R234 = 1.42*5.45 = 7.74 v

here,

v2=v3=v4=v234=7.74 v

and

I2=V2/R2= 7.74/10 = 0.774 A

I3=V3/R3 = 7.74/48 = 0.161 A

I4=V4/R4 = 7.74/16 = 0.484 A

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