An electric immersion heater is rated 5 A when connected to a 120V circuit. What is the resistance of the heater? If it takes 168 KJ to heat 500 ml of water from 20 deg C to boiling, how long does it take to heat the water?

R = V/I = 24 ohms

Power = V*I = 600 J/s

600*t = 168,000 J

Solve for t in seconds

To find the resistance of the electric immersion heater, we can use Ohm's law, which states that the resistance (R) of a device is equal to the voltage (V) across the device divided by the current (I) flowing through it.

Given that the current (I) is 5 A and the voltage (V) is 120V, we can use the formula:

R = V / I

Plugging in the values, we get:

R = 120V / 5 A = 24 Ω

So, the resistance of the heater is 24 Ω.

To determine how long it takes to heat the water, we need to use the formula for heat energy:

Q = mcΔT

where:
Q is the heat energy in Joules,
m is the mass of water in kilograms,
c is the specific heat capacity of water, and
ΔT is the change in temperature in degrees Celsius.

First, let's convert the mass of water from milliliters to kilograms. The density of water is 1 g/ml, so 500 ml of water is equivalent to 500 grams (or 0.5 kg).

Next, we need to find the change in temperature, ΔT. Given that the water is heated from 20°C to boiling, which is approximately 100°C, ΔT = 100°C - 20°C = 80°C.

Now, we can plug in the values into the formula:

Q = (0.5 kg) * (4.18 J/g°C) * (80°C)

Knowing that 1 kJ = 1000 J, we can convert the heat energy to kJ:

Q = (0.5 kg) * (4.18 J/g°C) * (80°C) / (1000 J/kJ) = 16.72 kJ

Finally, we can calculate the time it takes to heat the water using the formula:

Q = Pt

where:
P is the power in watts, and
t is the time in seconds.

Since power is the product of voltage and current (P = VI), and the voltage is 120V and the current is 5A, we can calculate the power:

P = (120V) * (5A) = 600W

Plugging in the values, we have:

16.72 kJ = (600W) * t

Converting 16.72 kJ to joules:

16.72 kJ * (1000 J/kJ) = 16,720 J

Now, we solve for t:

16,720 J = (600W) * t

t = 16,720 J / 600W

t ≈ 27.87 seconds

Therefore, it takes approximately 27.87 seconds to heat the water.