Question

Two resistors with values of 25 ohm and 35 ohm, respectively, are connected in series and hooked to a 12-V battery. a) There are 0.20 A current in the circuit b) There is 2.4 W power expended in the circuit. There is a box full of 25 Ohm and 35 Ohm resistors. How many resistors would be needed to make an equivalent resistance of 170 Ohm? How much power is dissipated in the 170 Ohm equivalent resistance if connected to the 12 Volt battery?

Answer 1

Given that, R1 = 25 ohm, R2 = 35 ohm

The two resistances are connected in series.

So, its equivalent resistance R = R1 + R2 = 25 + 35 = 60 ohm.

Batter voltage = 12 V

So, current I = V / R = 12 / 60 = 0.20 A

So, (a) is correct.

Power = I^2*R = 0.20^2*60 = 2.40 W

So, statement (b) is also correct.

To make 170 ohm resistance, connect 4 nos. of 25 ohm resistors in series.

And 2 nos. of 35 nos. resistors in series.

And connect these two combinations in series.

So, we neet total of 6 nos. of resistors (4 nos. 25 ohm + 2 nos. 35 ohm).

Power dissipated, P = I^2*R = V^2 / R = 12^2 / 170 = 0.847 Watt.