A 100W lamp bulb and a 4 kW water heater are connected to a 250V supply. Calculate 
(a) the current which flows in each appliance 
(b) the resistance of each appliance when in use. 
 Ans.[(a)0.4 A, 16 A, (b) 625 Ω, 15.26 Ω]


Data Given:


Power of the Lamp Bulb = P₁ = 100 W

Power of the Heater = P₂ = 4 KW = 4 ｘ 10³ W

Voltage of the power supply= V = 250 volts


To Find:


(a)
Current flowing through Lamp bulb = I₁ = ?
Current flowing through Heater = I₂ = ?

(b)
Resistance of Lamp bulb = R₁ = ?
Resistance of Heater = R₂ = ?



Solution:


(a)
To find Current I₁ flowing through the Lamp bulb 
by using formula P₁ = V I₁

I₁ = `\frac{P₁}{V}`

by putting values

I₁ = `\frac{100 W}{250 V}`

I₁ = 0.4 A---------------Ans. 1(a)

To find Current I₂ flowing through the heater
by using formula P₂ = V I₂

I₂ = `\frac{P₂}{V}`

by putting values

I₂ = `\frac{4 ｘ 10³ W}{250 V}`

I₂ = 0.016 ï½˜ 10³ W

I₂ = 16 ï½˜ 10⁻³ï½˜ 10³ W

I₂ = 16 A -----------------Ans.2(a)


(b)
According to Ohm's Law

V = I R

or

R = `\frac{V}{I}`

To find the resistance of Lamp bulb = R₁ 

R₁ = `\frac{V}{I₁}`

R₁ = `\frac{250 V}{0.4 A}`

R₁ = 625 Ω ----------------Ans. 1(b)



To find the resistance of heater = R₂

R₂ = `\frac{V}{I₂}`

R₂ = `\frac{250 V}{16 A}`

R₂ = 15.625 Ω -----------------Ans. 2(b)

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