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Assuming the resistance remains constant in this situation (a reasonable assumption) we can use ohms law where:

R = V / I (Resistance = Voltage / Current) Because we know that ohms law is a linear relationship (i.e. linear means if the voltage halfs the current halfs, if the voltage doubles the current doubles, if the voltage triples the current triples, etc…) we can express ohms law in terms of change in voltage (dv) and change in current (di) where: R = dv / di = (V1 - V2) / (I1 - I2) The question above already expresses the change in current (di = 1.53A) and expresses voltage (V1 = 14.2V and V2 = 5.64V) therefore: R = (14.2V - 5.64V) / 1.53A = 5.59ohms

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Q: The current in a resistor decreases by 1.53 A when the voltage applied across the resistor decreases from 14.2 V to 5.64 V Find the resistance of the resistor Answer in units of ohms?
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