Figure 9 shows some of the apparatus used in a demonstration of electrical power transmission using a dc power supply - AQA - A-Level Physics - Question 5 - 2020 - Paper 1

Since the lamps are connected in parallel, we first calculate the total resistance.

The total resistance of three identical lamps in parallel is given by:

rac{1}{R_{total}} = rac{1}{R_1} + rac{1}{R_2} + rac{1}{R_3}

Using the resistance from the previous part, we have:

rac{1}{R_{total}} = rac{1}{96} + rac{1}{96} + rac{1}{96} = rac{3}{96}

Thus,

R_{total} = rac{96}{3} = 32 ext{ Ω}

Now, applying Ohm's Law to find the current in the power supply:

I = rac{V}{R_{total}} = rac{12 ext{ V}}{32 ext{ Ω}} = 0.375 ext{ A}

So, the current in the power supply is approximately 0.38 A.

To calculate the resistance of each length of constantan wire, we use the formula:

ho rac{L}{A} $$ where: - $R$ = resistance - $ ho$ = resistivity of constantan = $4.9 imes 10^{-7} ext{ Ω m}$ - $L$ = length of constantan wire = 2.8 m - $A$ = cross-sectional area of the wire. First, we calculate the area (assuming a circular cross-section): $$ A = rac{ ext{π}}{4} d^2 $$ Substituting the diameter (converted to meters): - Diameter = 0.19 mm = 0.19 × 10^{-3} m So, $$ A = rac{ ext{π}}{4} (0.19 imes 10^{-3})^2 \ A ≈ 2.83 imes 10^{-8} m^2 $$ Now we calculate the resistance: $$ R = (4.9 imes 10^{-7}) rac{2.8}{2.83 imes 10^{-8}} ≈ 49.8 ext{ Ω} $$ Thus, each length of constantan wire has a resistance of about 50 Ω.

The demonstration is expected to show that the lamps are dimmer when connected using the long constantan wires compared to the short copper wires. To analyze this, we can compare the total resistance in both scenarios:

Using Short Copper Wires:

• Resistance is negligible, so total resistance remains 32 Ω.
• Current calculated is 0.375 A (each lamp receives maximum power).

Using Long Constantan Wires:

• Each constantan wire has a resistance of about 50 Ω.
• Total resistance with two wires:

$R_{total, constantan} = 32 + 2 imes 50 = 132Ω$

• Current through the power supply now becomes:

I_{constantan} = rac{12}{132} ≈ 0.091 A

Since current decreases, lamps receive less power:

• Power across lamps now would decrease further leading to them being dimmer.

Thus, the demonstration effectively shows lamps are significantly dimmer with the use of constantan wires.

Advantage:

• Superconductors exhibit zero electrical resistance, leading to no energy loss during transmission. This property allows for efficient power transmission over long distances without significant heating.

Difficulty:

• A major difficulty is maintaining ultra-low temperatures required to keep materials in their superconducting state. This makes practical utility highly challenging and costly, especially in long-distance applications.