Question #14427

The figure below shows two identical circuits connecting a 6V battery to an 18Ω resistor. The difference is that we chose to measure the voltages and currents in the two circuits differently: we used a different coordinate system of voltages and currents in our measurements.
You are to determine the voltages and currents indicated and compute the powers entering the elements.
What is the voltage (in Volts) v1 measured across the battery?
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What is the voltage (in Volts) v2 measured across the resistor?
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What is the current (in Amperes) i1 measured entering the battery?
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What is the current (in Amperes) i2 measured entering the resistor?
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What is the power (in Watts) P1=v1⋅i1 entering the voltage source?
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What is the power (in Watts) P2=v2⋅i2 entering the resistor?
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What is the voltage (in Volts) v3 measured across the battery?
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What is the voltage (in Volts) v4 measured across the resistor?
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What is the current (in Amperes) i3 measured entering the battery?
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What is the current (in Amperes) i4 measured entering the resistor?
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What is the power (in Watts) P3=v3⋅i3 entering the voltage source?
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What is the power (in Watts) P4=v4⋅i4 entering the resistor?
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Notice that the powers are the same in the two circuits. That is physical reality: power moves from the battery to the resistor, independent of the coordinate systems we use to measure the voltage and the current, so long as we use associated reference directions. We must always measure current into the terminal that we put the + sign of the voltage measurement on. Think of this as the red probe of the voltmeter.

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