Assume the equivalent resistance drops by 48.0%. Determine the value of R.

+2 votes

Consider the following circuit.

image

When the switch S in the circuit of the figure above is closed, will the equivalent resistance between points a and b increase or decrease?

    



State your reasoning.



Assume the equivalent resistance drops by 48.0%. Determine the value of R.
Ω

asked Feb 4, 2012 in Physics by yoshi ~Expert~ (919 points)
    

1 Answer

+2 votes
 
Best answer

The equivalent resistance would decrease because you would have twice as many resistors in parallel when the switch is closed.

The original resistance is:

R + 1 / (1/(90+10) + 1/(10+90))  = R + 50Ω

after closing the swtich the resistance becomes:

R + [1/ ((1/90) + (1/10))]  + [1/ ((1/10) + (1/90))]   = R + 18Ω

 

Now the question says the equivalent resistance drops by 48% so multiply the equation for the original resistance by 0.48 and set it equal to the second equation:

0.48*(R + 50Ω)  = R + 18Ω

now simplify and solve for R:

0.48R + 24Ω = R + 18Ω

R - 0.48R = 24Ω - 18Ω 

0.52R = 6Ω

R =  11.54Ω

 

 and you get that R =  11.54Ω

answered Feb 9, 2012 by awesome ~Expert~ (1,479 points)
selected Feb 9, 2012 by yoshi



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