A light bulb is rated 100 Watts for 220 Volts AC supply of 50 Hertz. Calculate(i) The resistance of the bulb(ii) The rms current through the bulb

To calculate the resistance of the bulb, we can use Ohm's law, which states that resistance (R) is equal to the voltage (V) divided by the current (I). In this case, we need to find the resistance based on the power rating and voltage of the bulb.

(i) Calculating the Resistance:
We know that power (P) is equal to voltage (V) multiplied by current (I). Therefore, we can rearrange the equation to solve for resistance:
P = V * I

Given:
Power (P) = 100 Watts
Voltage (V) = 220 Volts

Substituting the values into the equation:
100 = 220 * I

Solving for I:
I = 100 / 220
I ≈ 0.4545 Amperes

Now, we can use Ohm's law to calculate the resistance:
R = V / I
R = 220 / 0.4545
R ≈ 483.87 Ohms

Therefore, the resistance of the light bulb is approximately 483.87 Ohms.

(ii) Calculating the RMS Current:
To calculate the RMS (Root Mean Square) current through the bulb, we need to consider the power and resistance values. The RMS current (Irms) can be determined using the formula:
Irms = √(P / R)

Substituting the values into the equation:
Irms = √(100 / 483.87)
Irms ≈ √0.2064
Irms ≈ 0.4545 Amperes

Therefore, the RMS current through the bulb is approximately 0.4545 Amperes.