Question

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

Answer 1

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

$E = (r + R) i$

here we have 9 ohm resistance draw current of 0.80 A

$E = (9 + r)(0.80)$

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

$E = (17 + r)(0.50)$

so we will have

$8.5 + 0.50 r = 7.2 + 0.80 r$

$0.30 r = 1.3$

$r = 4.33 ohm$

also we have

$E = 10.67 V$

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

$10.67 = (R + 4.33)(0.12)$

so we have

$R = 84.5 ohm$