The antenna broadcasts radio signals at the resonant frequency of the tank circuit. Suppose that a certain tank circuit in a shortwave radio transmitter has a fixed capacitance of 1.8 x 10-11 F and a variable inductance. If the antenna is intended to broadcast radio signals ranging in frequency from 3.1 MHz to 9.2 MHz, find the (a) minimum and (b) maximum inductance of the tank circuit.

A straight path is inclined at an angle of 15 degree to the horizontal. A loaded skip of total mass 1500 kg is at rest on the path and is attached to a wall at the top of the path by a rope. The rope is taut and parallel to a line of greatest slope of the path, as shown in the diagram. Calculate the normal and rictional components of the contact force exerted on the skip by the path when the tension in the rope is 2000 N.

After the rope is cut the skip is on the point of slipping down the path. Calculate the coefficient of the friction between the skip and the path

To find the minimum and maximum inductance of the tank circuit, we need to use the resonant frequency formula for a tank circuit:

Resonant frequency (fr) = 1 / (2π√(LC))

where fr is the resonant frequency, L is the inductance, and C is the capacitance.

For the minimum frequency (fmin = 3.1 MHz), we can substitute the values into the formula:

3.1 x 10^6 Hz = 1 / (2π√(Lmin × 1.8 x 10^-11 F))

To find the minimum inductance, we can rearrange the formula to solve for Lmin:

Lmin = (1 / ( (2π × fmin)² × C ))

Plugging in the given values:

Lmin = (1 / ( (2π × 3.1 × 10^6 Hz)² × 1.8 x 10^-11 F ))

Calculating this will give you the minimum inductance.

Next, for the maximum frequency (fmax = 9.2 MHz), we can repeat the same process:

9.2 x 10^6 Hz = 1 / (2π√(Lmax × 1.8 x 10^-11 F))

Rearranging the formula to solve for Lmax:

Lmax = (1 / ( (2π × fmax)² × C ))

Substituting the given values:

Lmax = (1 / ( (2π × 9.2 × 10^6 Hz)² × 1.8 x 10^-11 F ))

Calculating this will give you the maximum inductance.

By plugging in the values and evaluating the equations, you can find the minimum and maximum inductance values for the tank circuit in the shortwave radio transmitter.