Two resistances, r1 and r2, are connected in series across a 12-v battery. the current increases by 0.20 a when r2 is removed, leaving r1 connected across the battery. however, the current increases by just 0.13 a when r1 is removed, leaving r2 connected across the battery. find (a) r1 and (b) r2.

The values of resistance r_1=33.3 ohm and r_2 = 41.7 ohm

The total resistance in series is the sum of the value of the resistances. Applying Ohm's law,

.....(1)

When the resistor r_1 is connected, the current increases by 0.2 A

Apply Ohm's law for the resistance r_1.

......(2)

When the resistor r_2 is connected, the current increases by 0.13 A.

Apply Ohm's law for the resistance r_2.

......(3)

From equations (1) and (2)

Similarly from equations (1) and (3), it can be seen that

From equations (4) and (5),

I=0.16 A

Substituting in equations (2) and (3)

a straight line sloped

an electric circuit