Charge, current, potential difference and resistance: Practice Questions

Which of the following best defines the electromotive force (e.m.f.) of a cell?

A circuit is constructed using four identical resistors, each with resistance \( R \). Three of the resistors are connected in parallel with each other. This parallel combination is then connected in series with the fourth resistor. What is the total equivalent resistance of the entire circuit?

Two wires, P and Q, are made of the same metal and carry the same electrical current. The diameter of wire P is twice the diameter of wire Q. What is the ratio of the drift velocity of the charge carriers in wire P to the drift velocity in wire Q?

A component has a potential difference of \( 12 \text{ V} \) across it when a current of \( 0.50 \text{ A} \) passes through it. What is the resistance of the component?

A metal wire of resistance \( R \) is stretched uniformly until its length is doubled. Assuming the density and resistivity of the metal remain constant during the process, what is the new resistance of the wire?

A potential divider circuit consists of a 12.0 V battery with negligible internal resistance, a fixed resistor of resistance \(R = 4.0\text{ k}\Omega\), and a negative temperature coefficient (NTC) thermistor. At room temperature, the resistance of the thermistor is \(8.0\text{ k}\Omega\).

(a) Calculate the output potential difference \(V_{out}\) across the thermistor at room temperature.
(b) The temperature of the thermistor increases. State and explain the effect this has on the value of \(V_{out}\).
(c) A student suggests that this circuit could be used to turn on a fan when the temperature exceeds a certain limit. If the fan requires at least 9.0 V to operate, calculate the resistance the thermistor must reach to trigger the fan.