What is the internal resistance of a cell if a current of 0.9 A flows through a 2 ohm resistor and a current of 0.3 A through a 7 ohm resistor?

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For a cell with an internal resistance of Rc, if it is connected to a resistor with resistance R, the current I that flows through R and the voltage of the cell V are related by:

V = (Rc + R)*I ... (1)

Now we have the current through a 2 ohm resistor given as 0.9 A and the current through a 7 ohm resistor given as 0.3 A.

Substituting these values in (1) we get

V = (Rc + 2)*0.9 and V = (Rc + 7)*0.3

Equating the two: (Rc + 2)*0.9 = (Rc + 7)*0.3

=> 0.9 Rc + 0.9*2 = 0.3 Rc + 7*0.3

=> Rc (0.9 - 0.3) = 2.1 - 1.8

=> Rc * 0.6 = 0.3

=> Rc = 0.3/0.6

=> Rc = 0.5 ohm

Therefore the internal resistance of the cell is equal to 0.5 ohm.

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