Electric Circuits: Current, Resistance and Circuit Laws: Practice Questions

Which of the following statements correctly describes the change in resistance for a negative temperature coefficient (NTC) thermistor as its temperature increases?

A potential divider circuit consists of a DC supply with negligible internal resistance, a fixed resistor \(R_1\), and a light-dependent resistor (LDR) connected in series. The output voltage \(V_{out}\) is measured across the fixed resistor \(R_1\). If the light intensity shining on the LDR increases, what happens to the output voltage \(V_{out}\)?

A circuit consists of three identical resistors, each of resistance \( R \). Two of the resistors are connected in parallel, and this combination is connected in series with the third resistor and a battery of e.m.f. \( E \) (negligible internal resistance). What is the power dissipated in one of the two parallel resistors?

A steady current of \( 2.0\text{ A} \) flows through an electrical circuit for a period of \( 1.5\text{ minutes} \). What is the total charge that passes through any point in the circuit during this time interval?

At a junction in a DC circuit, three wires meet. Wire 1 carries a current of \( 4.5\text{ A} \) directed into the junction. Wire 2 carries a current of \( 2.8\text{ A} \) directed out of the junction. What are the magnitude and direction of the current in Wire 3?

State Kirchhoff’s first law and identify the physical quantity whose conservation is the basis for this law.

A potential divider circuit is connected to a \( 10.0 \, \text{V} \) supply. It consists of a fixed resistor \( R_1 = 200 \, \Omega \) and a light-dependent resistor (LDR) in series. Calculate the output voltage across the LDR when its resistance is \( 800 \, \Omega \).

A potential divider circuit consists of a cell with e.m.f. \(6.0\,\text{V}\) and internal resistance \(2.0\,\Omega\) connected in series with a \(10.0\,\Omega\) fixed resistor and a thermistor. If the potential difference measured across the \(10.0\,\Omega\) resistor is \(4.0\,\text{V}\), calculate the resistance of the thermistor at this temperature.

A student has two wires, X and Y, made of different materials. Wire X is an ohmic conductor, while wire Y is a filament lamp.

(a) Sketch the current-potential difference (\(I-V\)) graphs for both components on the same axes.
(b) Explain the shape of the graph for wire Y in terms of the behavior of ions and electrons within the material as the potential difference increases.

A high-resistance voltmeter is used to measure the electromotive force (e.m.f.) of a battery, giving a reading of \( 9.40\text{ V} \). When the battery is connected to an external load resistor of \( 15.0\text{ }\Omega \), the reading on the voltmeter drops to \( 8.70\text{ V} \).

(a) Define the term terminal potential difference and explain why it is lower than the e.m.f. in this circuit.
(b) Calculate the current flowing through the external resistor.
(c) Calculate the internal resistance \( r \) of the battery.
(d) Determine the efficiency of the circuit (the ratio of power delivered to the load to the total power supplied by the battery).