Question

two heater coils rated 500 watt 220 volt and 100 watt 220 volt are connected in series find the net power of the combined heating coil

Answer 1

Explanation :

Power of first coil, P₁ = 500 Watt

Voltage of first coil, V₁ = 220 V

Power of second coil, P₂ = 100 Watt

Voltage of second coil, V₂ = 220  V

Power is given by :

$P_1=\dfrac{V_1^2}{R_1}$

$R_1=\dfrac{V_1^2}{P_1}$

$R_1=\dfrac{220^2}{500}\Omega$

$R_1=96.8\ \Omega$

Similarly,

$P_2=\dfrac{V_2^2}{R_2}$

$R_2=\dfrac{V_2^2}{P_2}$

$R_1=\dfrac{220^2}{100}\Omega$

$R_1=484\ \Omega$

So, taking series combination of these two resistors as :

$\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

$\dfrac{1}{R_{eq}}=\dfrac{1}{484}+\dfrac{1}{96.8}$

$R_{eq}=83.34\ \Omega$

Net power is given by :

$P=\dfrac{V^2}{R}$

$P=\dfrac{220^2}{83.34}$

$P=581\ Watts$

Hence, this is the required solution.