Resistance is an electrical property that opposes the flow of electric current through a conductor. Conductors are classified into ohmic conductors, which obey Ohm’s Law, and non-ohmic conductors, which do not. The resistance of a conductor is influenced by physical factors such as length, cross-sectional area, material resistivity, and temperature. Understanding resistance allows for the analysis of series and parallel combination circuits, as well as the practical selection of materials for heating elements, household wiring, and high-efficiency superconducting devices.
Link the physical parameters \(l\), \(A\), and \(\rho\) to the formula \(R = \frac{\rho l}{A}\), and distinguish between ohmic and non-ohmic \(V\)-\(I\) characteristic graphs.
An ohmic conductor obeys Ohm’s Law. Its graph of \(V\) against \(I\) is a straight line passing through the origin. Example: constantan wire at constant temperature.
A non-ohmic conductor does not obey Ohm’s Law. Its graph of \(V\) against \(I\) is a curve with an increasing gradient. Example: filament bulb.
Current is the same through each resistor: \(I = I_1 = I_2 = I_3\). Total potential difference: \(V = V_1 + V_2 + V_3\). Effective resistance: \(R = R_1 + R_2 + R_3\).
Total current: \(I = I_1 + I_2 + I_3\). Potential difference is the same across each branch: \(V = V_1 = V_2 = V_3\). Effective resistance: \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\).
Resistance of a wire
Where \(R\) is resistance in \(\Omega\), \(\rho\) is resistivity in \(\Omega\text{ m}\), \(l\) is length in \(\text{m}\), and \(A\) is cross-sectional area in \(\text{m}^2\).
Answer in your mind, then press “Check Answer”.
What happens to the resistance of a filament bulb as the current flowing through it increases? Explain why.
Two identical constantan wires, each of length \(50\text{ cm}\) and resistance \(4\ \Omega\), are connected in parallel. What is the effective resistance of the combination?
A wire of length \(2.0\text{ m}\) with a cross-sectional area of \(1.0 \times 10^{-6}\text{ m}^2\) has a resistance of \(3.4\ \Omega\). What is the resistivity of the wire material?
Standard Wire Gauge (s.w.g.) increases as wire thickness increases.
A higher s.w.g. number actually denotes a thinner wire with a smaller diameter and cross-sectional area.
Tungsten is inherently non-ohmic under all conditions.
Tungsten wire is an ohmic conductor when its temperature is kept constant. It only displays non-ohmic behavior in a bulb because its temperature rises significantly during operation.
Superconductors reduce resistance to a tiny value close to zero.
At or below the critical temperature (\(T_c\)), the electrical resistivity of a superconductor is strictly zero, meaning current flows without any loss of energy as heat.
Objective: Test your understanding of resistance, resistivity, and material classification.
1 Which of the following statements correctly describes a tungsten filament bulb during operation?
2 What happens to the resistance of a constantan wire if its length is doubled and its cross-sectional area is halved at constant temperature?
3 The SI unit for the resistivity of a conductor is the .
4 The temperature at which the resistivity of a superconductor becomes zero is called the temperature.
Match each electrical material or component to its correct characteristic or function based on its resistivity. If using a phone, tap the answer first, then tap the matching box.
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