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1.1 Ohm's law relates V , I, and R for a resistor. For each of the situations following, find the missing item: (a) R = 1 k, V = 5 V (b) V = 5 V, I = 1 mA (c) R = 10 k, I = 0.1 mA (d) R = 100 , V = 1 V Note: Volts, milliamps, and kilohms constitute a consistent set of units.
A discussion is made of the equations and boundary conditions that govern the flow of electric current in solids under applied voltages. The electrical resistance of a sphere is calculated as an example, apparently for the first time since the introduction of the concept in 1879. The linear relationship between potential difference and electric current across a segment of circuit of arbitrary shape is discussed. The linear constant, the resistance, is explicity expressed in terms of some effective length and cross-section.
Start from the right hand side of the circuit and make series and parallel combinations of the resistors until one equivalent resistor remains. Begin by combining the 6 Ω resistor and the 10 Ω resistor in series: 6 Ω + 10 Ω = 16 Ω Now combine this 16 Ω resistor in parallel with the 64 Ω resistor: 16 Ω64 Ω = (16)(64) 16 + 64 = 1024 80 = 12.8 Ω This equivalent 12.8 Ω resistor is in series with the 7.2 Ω resistor: 12.8 Ω + 7.2 Ω = 20 Ω Finally, this equivalent 20 Ω resistor is in parallel with the 30 Ω resistor: 20 Ω30 Ω = (20)(30) 20 + 30 = 600 50 = 12 Ω Thus, the simplified circuit is as shown: 3–1
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