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## Q. 1.4

Consider a circuit involving a 10V voltage source connected to a 5 Ω resistor.

## Verified Solution

Note that voltage and current directions are defined arbitrarily, but they must obey the
sign convention.We can analyze the circuit as follows.
• Using the definition of the voltage source:$v_{s}$ = 10V.
• Using the definition of the voltage between two points and considering that the voltage
is fixed along a wire: $v_{R}$ = $v_{s}$ = 10V.
• Using the definition of the resistor (Ohm’s law):$i_{R}$ = $v_{R}$∕5 = 2V.
• Using the definition of the current: $i_{s}$ = −$i_{R}$ = −2A.
• Using the definition of the power: $p_{s}$ = $v_{s}$$i_{s}$ = −20W.
• Using the definition of the power: $p_{R}$ = $v_{R}$$i_{R}$ = 20W.
The signs of power values indicate that the voltage source delivers energy, while the
resistor consumes the same amount of energy. As expected, we have $p_{s}$+ $p_{R}$ = 0 due to
the conservation of energy.