The root means square value of an a.c. mains supply is 220 V. Calculate its peak voltage

The weight of the elevator acts downwards, and the tension in the cable acts upwards. Since the elevator is accelerating downwards, the net force is downwards.
The net force is given by Newton's second law: $F_{net} = ma$.
The forces are:
Weight ($W$) = $mg$ (downwards)
Tension ($T$) (upwards)
Since the acceleration ($a$) is downwards, the equation of motion is:

mass ($m = 1000 \, \text{kg}$), acceleration due to gravity ($g = 10 \, \text{m/s}^2$), and elevator's acceleration ($a = 1.0 \, \text{m/s}^2$).

The tension in the cable is $\boxed{\text{C. } 9,000 \, \text{N}}$.

Rounding to the nearest whole number, the peak voltage is $311 \, \text{V}$.
The peak voltage is $\boxed{\text{D. } 311 \, \text{V}}$.

The circuit consists of a battery ($V = 3.0 \, \text{V}$), a fixed resistor ($R_1 = 5 \, \Omega$), and a rheostat ($R_{rheostat}$). The desired current is $I = 0.25 \, \text{A}$. The internal resistance of the battery is negligible.

The resistance of the rheostat must be adjusted to $\boxed{\text{B. } 7 \, \Omega}$.