A transformer's secondary coil contains 100 turns and operates at 10 volts. If the turns ratio is 18:1, find (a) the voltage ratio, (b) the primary voltage, and (c) the number of primary turns.

The turns ratio $\frac{N_p}{N_s}$ is $18:1$.

For an ideal transformer, the voltage ratio is equal to the turns ratio.

The voltage ratio is $\boxed{\mathbf{18:1}}$.

Given $V_s = 10 \text{ V}$.

The primary voltage is $\boxed{\mathbf{180 \text{ V}}}$.

Given $N_s = 100 \text{ turns}$.

The number of primary turns is $\boxed{\mathbf{1800 \text{ turns}}}$.

6. A 110-volt alternating current line is fed through a 55-turn step-down autotransformer. If you want a 28-volt output, find the secondary turns and the turn number to tap.

For an autotransformer, the ratio of voltages is equal to the ratio of the number of turns.

For a step-down autotransformer, the secondary turns represent the tap point from the common end.
The secondary turns are $\boxed{\mathbf{14 \text{ turns}}}$ and the turn number to tap is $\boxed{\mathbf{14}}$.

7. When two coils are put near together, a changing current in the first coil induces a voltage in the second. This phenomenon is called:

This phenomenon is called mutual induction.

8. Two inductive coils near each other have a mutual inductance of 0.6H. Current across one coil is boosted from 1A to 6A in 0.03 seconds. The voltage induced in the other coil is:

The magnitude of the induced voltage ($\mathcal{E}$) in the second coil due to a changing current in the first coil is given by $\mathcal{E} = M \frac{\Delta I}{\Delta t}$.

The voltage induced in the other coil is $\boxed{\mathbf{100 \text{ V}}}$.

9. Two identical coils, A and B, with 400 turns set so that 60% of the flux produced by one coil connects to the other. Calculate the mutual inductance between coils A and B if a current of 10A runs through coil A, producing a flux of 20mWb.

Mutual inductance ($M$) is defined as $M = \frac{N_B \Phi_{BA}}{I_A}$, where $N_B$ is the number of turns in coil B, $\Phi_{BA}$ is the flux linked with coil B due to current $I_A$ in coil A.

The flux linked with coil B is 60% of the flux produced by coil A:

The mutual inductance between coils A and B is $\boxed{\mathbf{0.48 \text{ H}}}$.