Question

1. calculate use ohms law to find the voltage needed to make a current of 3 a in a resistance of 9 ω. show your work
2. calculate how much electrical energy, in kilowatt-hours, does a 200 w light bulb use if it is left on for 13 h? show your work
3. apply concepts why does increasing the voltage of a wire have the same effect on the current that decreasing the resistance has?

Explanation:

Question 3

Step1: Recall Ohm's law formula

Ohm's law is \(V = IR\), where \(V\) is voltage, \(I\) is current, and \(R\) is resistance.

Step2: Substitute the given values

Given \(I = 3\space A\) and \(R=11\space\Omega\). Substitute into the formula: \(V=(3\space A)\times(11\space\Omega)\)

Step3: Calculate the voltage

\(V = 33\space V\)

Step1: Convert power to kilowatts

The power of the bulb \(P = 200\space W=0.2\space kW\) (since \(1\space kW = 1000\space W\)).

Step2: Use the energy formula \(E=Pt\)

The time \(t = 13\space h\). Substitute \(P = 0.2\space kW\) and \(t = 13\space h\) into \(E=Pt\). So \(E=(0.2\space kW)\times(13\space h)\)

Step3: Calculate the energy

\(E = 2.6\space kWh\)

According to Ohm's law \(I=\frac{V}{R}\). When \(V\) increases (assuming \(R\) is constant), \(I\) increases. When \(R\) decreases (assuming \(V\) is constant), \(I=\frac{V}{R}\) also increases. Mathematically, increasing \(V\) (numerator) and decreasing \(R\) (denominator) both lead to an increase in \(I\) based on the relationship \(I=\frac{V}{R}\)

Answer:

\(33\space V\)

Question 4