A resistor is connected to a power supply - Edexcel - GCSE Physics Combined Science - Question 5 - 2018 - Paper 1

To calculate the time, we use the formula for current which is defined as the charge divided by time:

$I = \frac{Q}{t}$

Rearranging gives us

$t = \frac{Q}{I}$

Here, the total charge Q is 42C and the current I is 200mA (or 0.2A). Thus,

$t = \frac{42}{0.2} = 210 \, \text{seconds}.$
Now converting seconds to minutes, we have 210 / 60 = 3.5 minutes.

The energy transferred can be calculated using the formula:

$E = V \cdot Q$

Where E is the energy, V is the potential difference, and Q is the charge. Substituting the known values gives us:

$E = 6.0 \, \text{V} \cdot 42 \, \text{C} = 252 \, \text{J}.$

The resistor becomes warm due to collisions between the flowing electrons (which carry current) and the fixed lattice structure of the resistor. As current flows, the electrons gain kinetic energy and collide with atoms in the lattice, causing them to vibrate more. This increased vibration leads to a rise in thermal energy, making the resistor warm.

The potential difference between points P and Q is given as 6.0V with a current of 1.2A flowing through the circuit. If we consider the two resistors of 100 ohms each:
If the resistors were in series, the total resistance would be 200 ohms. Using Ohm's law, we get:

$V = I \times R => 6.0 = 1.2 \times 200$

This leads to a voltage of 240V, which exceeds 6V, indicating that they cannot be in series.

For parallel, the total resistance R can be calculated as:

$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{100} + \frac{1}{100} = \frac{2}{100} = \frac{1}{50}$

Thus, R = 50 ohms. Substituting back into Ohm's law gives:

$I = \frac{V}{R} = \frac{6.0}{50} = 0.12 \, \text{A}$

Since we have 1.2A, the resistors must be connected in parallel to allow for such a current at the given voltage.