A step-down transformer that converts 120 V AC to 10.0 V AC (rms values), and the secondary winding is connected to a purely resistive circuit having an equivalent resistance of 2.00 . a. What is the output rms current to the circuit?

a. The output rms current to the circuit can be calculated using the formula: {eq}I_{rm rms} = \frac{V_{rm rms}}{R_{rm eq}} {/eq} where {eq}V_{rm rms} = 10.0\text{ V} {/eq} and {eq}R_{rm eq} = 2.00 , Omega {/eq}. Plugging these values into the formula, we get: {eq}I_{rm rms} = \frac{10.0\text{ V}}{2.00 , Omega} = 5.00 \text{ A} {/eq} Therefore, the output rms current to the circuit is 5.00 A. b. The input rms current to the primary coil can be calculated using the formula: {eq}frac{V_{rm primary}}{V_{rm secondary}} = \frac{N_{rm primary}}{N_{rm secondary}} {/eq} where {eq}V_{rm primary} = 120 \text{ V} {/eq}, {eq}V_{rm secondary} = 10.0 \text{ V} {/eq}, {eq}N_{rm primary} {/eq} is the number of turns in the primary coil, and {eq}N_{rm secondary} {/eq} is the number of turns in the secondary coil. Since the transformer is a step-down transformer, {eq}N_{rm secondary} < N_{rm primary} {/eq}. We can rearrange this formula to solve for {eq}I_{rm primary} {/eq}, the input rms current to the primary coil: {eq}I_{rm primary} = I_{rm secondary}left\frac{N_{rm secondary}}{N_{rm primary}}right) {/eq} where {eq}I_{rm secondary} = I_{rm rms} = 5.00 \text{ A} {/eq}. We can calculate the ratio {eq}frac{N_{rm secondary}}{N_{rm primary}} {/eq} using the formula: {eq}frac{V_{rm primary}}{V_{rm secondary}} = \frac{N_{rm primary}}{N_{rm secondary}} {/eq} Rearranging this formula, we get: {eq}frac{N_{rm secondary}}{N_{rm primary}} = \frac{V_{rm secondary}}{V_{rm primary}} {/eq} Plugging in the values, we get: {eq}frac{N_{rm secondary}}{N_{rm primary}} = \frac{10.0 \text{ V}}{120 \text{ V}} = 0.0833 {/eq} Therefore, the input rms current to the primary coil is: {eq}I_{rm primary} = 5.00\text{ A} left\frac{0.0833}{1}right) = 0.416 \text{ A} {/eq} Therefore, the input rms current to the primary coil is 0.416 A.