A 12 V battery supplies a current of 0.5 A to a lamp for 2 minutes. Calculate (a) the charge passing through the battery, (b) the energy transferred by the battery, and (c) the resistance of the lamp.

The current $I$ is $0.5 \, \text{A}$ and the time $t$ is $2 \, \text{minutes}$. First, convert the time to seconds.

The formula for charge $Q$ is $Q = I \times t$.

The charge passing through the battery is $\boxed{\text{60 C}}$.

The voltage $V$ is $12 \, \text{V}$ and the charge $Q$ is $60 \, \text{C}$ (from Step 1).
The formula for energy transferred $E$ is $E = V \times Q$.

The energy transferred by the battery is $\boxed{\text{720 J}}$.

The voltage $V$ across the lamp is $12 \, \text{V}$ and the current $I$ through it is $0.5 \, \text{A}$.
Using Ohm's Law, $R = \frac{V}{I}$.

The resistance of the lamp is $\boxed{\text{24 } \Omega}$.

Radioactivity is the spontaneous emission of radiation (such as alpha particles, beta particles, or gamma rays) from the nucleus of an unstable atom. This process results in the transformation of the unstable nucleus into a more stable one.

Thorium-232 ($\text{Th}^{232}_{90}$) emits two beta particles ($^0_{-1}e$).
Let the daughter nucleus be $\text{X}^A_Z$.
The decay equation is:

To conserve the mass number ($A$):

To conserve the atomic number ($Z$):

The element with atomic number 92 is Uranium (U).
So the daughter nucleus is $\text{U}^{232}_{92}$.
The decay equation is:

The daughter element is $\text{U}^{232}_{92}$.

• The number of protons is equal to the atomic number ($Z$).

• The number of neutrons is equal to the mass number ($A$) minus the atomic number ($Z$).

The daughter element has $\boxed{\text{92 protons}}$ and $\boxed{\text{140 neutrons}}$.

To draw the velocity-time graph:

• Plot time (s) on the x-axis and velocity (m/s) on the y-axis.
• Use the given data points from Table C1.1: (0 s, 0 m/s) (5 s, 10 m/s) (10 s, 20 m/s) (15 s, 30 m/s) (20 s, 30 m/s) (25 s, 30 m/s) (30 s, 30 m/s) (35 s, 15 m/s) (40 s, 0 m/s)
• Connect the plotted points with straight lines. The graph will show an initial increase in velocity, followed by a period of constant velocity, and then a decrease in velocity back to zero.