Question

A certain brand of hot dog cooker applies a potential difference of $120\mathrm{V}$ to opposite ends of the hot dog and cooks it by means of the heat produced. If $48\mathrm{kJ}$ is needed to cook each hot dog, what current is needed to cook three hot dogs simultaneously in $2.0\min$ ? Assume a parallel connection.

Short answer

Answer: The current needed to cook three hot dogs simultaneously in 2.0 minutes is 10 A.

Step-by-step solution

Convert time to seconds

Since we are given the time in minutes, we need to convert it into seconds for our calculations. We can do this by multiplying the given time by 60: 2.0 minutes * 60 seconds/minute = 120 seconds

Calculate the total energy needed

We know that 48 kJ of energy is needed to cook one hot dog, so to cook three hot dogs simultaneously, we need to multiply the energy required for one hot dog by three: 3 hot dogs * 48 kJ/hot dog = 144 kJ Now, convert the energy from kilojoules to joules: 144 kJ * 1000 J/kJ = 144000 J

Use the power formula to find the required power

We can use the formula for electrical power, P = E/t, where E is the total energy and t is the time taken. In this case, E = 144000 J and t = 120 seconds: P = 144000 J / 120 s = 1200 W

Calculate the current

Now that we have the required power (P), we can use the formula for electrical power to find the current (I). The formula is P = VI, where V is the potential difference and P is the power. We are given a potential difference of 120V: 1200 W = I * 120V Divide both sides by 120V to find the current (I): I = 1200 W / 120 V = 10 A So, a current of 10 A is needed to cook three hot dogs simultaneously in 2.0 minutes using the given hot dog cooker.