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An airplane black box contains a bunch of unknown resistances and batteries con- nected in unknown way such that (1) a 9 Ohm resistor across the terminals of the circuit box draws 0.80 A, and (2) an 17 Ohm resistor draws 0.50 A. What resistance will draw 0.12 A

Respuesta :

Answer:

The unknown resistance which will draw a current of 0.12 A is 84.5 ohm

Explanation:

Let say the emf of the cell is E and internal resistance of the system is "r"

now we will have

[tex]E = (r + R) i[/tex]

here we have 9 ohm resistance draw current of 0.80 A

[tex]E = (9 + r)(0.80)[/tex]

also we know that 17 ohm resistance will draw current of 0.50 A

[tex]E = (17 + r)(0.50)[/tex]

so we will have

[tex]8.5 + 0.50 r = 7.2 + 0.80 r[/tex]

[tex]0.30 r = 1.3[/tex]

[tex]r = 4.33 ohm[/tex]

also we have

[tex]E = 10.67 V[/tex]

now when 0.12 A current is drawn across unknown resistance then we have

[tex]10.67 = (R + 4.33)(0.12)[/tex]

so we have

[tex]R = 84.5 ohm[/tex]

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