As electrons move through a metal, the metal resists this movement - Leaving Cert Physics - Question 9 - 2021

The instrument used to measure resistance is called an ohmmeter.

The relationship between resistance and length can be stated as follows:

Resistance is directly proportional to the length of the conductor. Thus, if the length doubles, the resistance also doubles. Mathematically, this can be expressed as:

$R \propto L$

where $R$ is resistance and $L$ is length.

To calculate the circular cross-sectional area ($A$) of the wire, we use the formula:

$A = \pi r^2$

Here, the radius $r$ is given as 0.2 mm, which converts to 0.2 × 10⁻³ m. Therefore:

$A = \pi (0.2 \times 10^{-3})^2 = 1.26 \times 10^{-7} \ m^2$

The resistance of the wire can be calculated using the formula:

$R = \frac{\rho L}{A}$

Where:

• $\rho = 1.1 \times 10^{-6} \ \Omega m$ (resistivity of nichrome)
• $L = 4.8 \ m$
• $A = 1.26 \times 10^{-7} \ m^2$ (cross-sectional area)

Substituting the values:

$R = \frac{1.1 \times 10^{-6} \times 4.8}{1.26 \times 10^{-7}} \approx 4.20 \ \Omega$

For resistors in parallel, the total resistance ($R_t$) is given by:

$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Given:

• $R_1 = 5 \ \Omega$
• $R_2 = 3 \ \Omega$
• $R_3 = 4 \ \Omega$

Calculating:

$\frac{1}{R_t} = \frac{1}{5} + \frac{1}{3} + \frac{1}{4} = 0.20 + 0.33 + 0.25 = 0.78$

Then:

$R_t = \frac{1}{0.78} \approx 1.05 \ \Omega$

After calculating the total resistance for resistors in parallel as 1.05 Ω, if any additional resistances are in series, they must be added. Assuming, for example, that a resistor of 3 Ω is in series, the total resistance ($R_{total}$) will be:

$R_{total} = R_t + R_{series} \approx 1.05 + 3.00 = 4.05 \Omega$

To find the current ($I$) flowing through the ammeter, we can use Ohm's law:

$I = \frac{V}{R}$

Where:

• $V = 12 \ V$ (voltage of the circuit)
• $R \approx 4.05 \ \Omega$ (total resistance)

Thus:

$I = \frac{12}{4.05} \approx 2.96 \ A$

The wire labelled P is yellow and green, which indicates it is the earth wire. Its function is to provide a safe path for excess current to flow into the ground, thereby preventing electrical shock and ensuring safety.

The wire labelled Q is typically referred to as the neutral wire.