Problem: A circuit has a source that creates a constant 10.25 Volt potential difference across series resistances of 3.2 Ohms and 3.35 Ohms. What is the current through the source, and how much does the voltage change across the first, and across the second, resistor?
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Solution: Since the current must go through both resistors, it will experience the total resistance 3.2 ohm + 3.35ohm = 6.55 ohm. The current must therefore be ( 10.25 Volts)/( 6.55 Ohms) = 1.564 Amps. The voltage change associated with 1.564 Amps through 3.2 ohm is ( 1.564 Amps)( 3.2 ohm) = 5 Volts; through the 3.35 ohm resistor the change is ( 1.564 Amps)( 3.35 ohm) = 5.2 Volts. Note that these results add up to the original voltage.
Generalized Response:
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Figure description: The figure below charts the relationships among voltage, resistance, current and power. The 'blue' triangle shows how voltage, current and resistance are related. (Greater voltage or less resistance implies greater current, reflecting I = V / R; resistance is the ratio of voltage to current, reflecting R = V / I; a current I through a resistance R requires a greater voltage drop pfor a greater current and for a greater resistance, reflecting V = I * R).
The 'green' triangle shows how power is the product of current and voltage (current is measured in C / s, voltage in J / C, so the product of current and voltage is the number of J / s, or watts, of power).
The relationship P = I * V can be combined with either I = V / R or with V = I * R to yield either P = I * (I * R) = I^2 * R or P = (V / R ) * V = V^2 / R.
