Problem — true or false on resistive circuits

Problem

True or false? (a) In a purely resistive circuit the current is in phase with the voltage. (b) In series the currents add up, in parallel the voltages add up. (c) The sum of the currents entering a node equals the sum of those leaving it. (d) The SI unit of resistance is the ohm. (e) The power dissipated in a resistor is $P = I/V$.

Solution

(a) TRUE. In a pure resistor there is no phase shift between current and voltage: $v = R\,i$ at every instant, so current and voltage reach their maxima and zeros at the same instants (they are in phase). A phase shift only appears with capacitors or inductors.

(b) FALSE. It is exactly the opposite: in series the current is the same in all elements and the voltages add up; in parallel the voltage is the same and the currents add up.

(c) TRUE. This is Kirchhoff’s first law (the node law), a consequence of charge conservation: charge does not accumulate at a node, so $\sum i_\text{in} = \sum i_\text{out}$.

(d) TRUE. The SI unit of resistance is the ohm ($\Omega$), defined as $1\ \Omega = 1\ \text{V}/1\ \text{A}$.

(e) FALSE. The power dissipated is $P = V\,I$ (a product, not a quotient), equivalent to $P = R\,I^2 = V^2/R$. The form $I/V$ is dimensionally wrong.

$\ev{\text{T, F, T, T, F}}$

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Topics: Circuiti elettrici Concepts: Leggi di Kirchhoff · Legge di Ohm