When a resistor is connected to a 12-V source, it draws a 185-mA current. The same resistor connected to a 90-V source draws a 1.25-A current. (a) Is the resistor ohmic? Justify your answer mathematically. (b) What is the rate of Joule heating in this resistor in both cases?

Ohm's law is define by the formula

V = IR where I is current in A, R is resistance in ohms

to calculate the resistance we use the formula above

I = 185 mA / 1000 = 0.185 A

case 1, R = V / I = 12 V / 0.185 A = 64.86 ohms

case 2, R = V / I = 90 / 1.25 A = 72 ohms

a) the resistor is not ohmic since there is no linear relationship between R and V (as voltage increases, resistance ought to also increase)

b) rate of Joule heating in the case 1, P, power = IV = 0.185 A * 12 = 2.22 W

case 2, P = IV = 1.25 A * 90 V = 112.5 W

The resistor is not Ohmic

Explanation:

In the first case, from ohm's law: V=IR

R=V/I = 12/0.185=64.9 ohm

In the second case:

R=V/I = 90/1.25 = 72ohm

The relationship between voltage and current is linear according to ohms law but that is not the case here.

Joule heating = I^2R

For case1: (0.185) ^2 * 64.9 = 2.2W

For case2: (1.25) ^2 * 72 = 112.5W