Which resistor dissipates the most power?

Question

Three resistors having resistance of 1.60Ω, 2.40Ω, and 4.80Ω are connected in parallel to a 28.0V battery that has negligible internal resistance.Which resistor dissipates the most power: the one with the greatest resistance or the least resistance?

Explain why this should be.

Answer 1

to tell which the resistor is, u hv to do calculations.

the effective resistance in parallel is Rp = 1.6||2.4||4.8 = 1.25

so, the total current is, I = 28V / 1.25 = 22.4A

now, find the current flowing thru each of the resistors and

then use the formula, P = I^2 * R

R1 = 1.6 ;

I1 = 0.5 * 22.4A = 11.2A

P1 = 11.2^2 * 1.6 = 200.7W

R2 = 2.4 ;

I2 = 0.33 * 22.4A =  7.46A

P2 = 7.46^2 * 2.4 = 133.56W

R3 = 4.8 ;

I3 = 0.1667 * 22.4A = 3.733A

P3 = 3.733^2 * 4.8 = 66.89W

so, now u can say that the lowest resistance dissipates the highest power.

if u r wondering how i got the terms, 0.5, 0.33, 0.1667 ; its like this. observe that 1.6, 2.4, 4.8 are in the ratio of 2:3:6.

to find current thru R1, consider resistances R2 and R3 as one resistance. so, now u hv 1.6 and 1.6 (2.4||4.8) in parallel. so current thru R1 is 0.5 times the total current, i.e., 0.5*22.4 = 11.2A.  similarly, u'll get the other terms...