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12 March, 08:00

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?

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  1. 12 March, 08:20
    0
    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
  2. 12 March, 08:23
    0
    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
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