Question

A heater coil is cut into two equal parts and only one part is used in the heater. The heat generated now for the same current will be ________
1. Doubled
2. Four times
3. One fourth
4. Half

Answer 1

Correct Answer - Option 1 : Doubled

Concept:

Resistance:

• The property of electrical materials and electrical instruments that opposes the flow of current through them is called resistance.
• It is denoted by R. The SI unit of resistance is the ohm (Ω).
• It is given as R = V / I

V is voltage or potential difference, I is the current.

• Resistance is directly proportional to the length of the conductor. 

R ∝ l

Electric Power

Electric power is the rate of consumption of electric energy in any device. 

It is denoted as 

P = I² R = V² / R = V × I

Explanation:

In-home appliances, the potential difference is supplied at 220 V, 50 Hz. 

The connections are made in parallel. 

The average voltage is approximately maintained at this ratio. 

Now, 

P = I2 R = V2 / R

\(\implies P ∝ \frac{1}{R}\)

So, Power is inversely proportional to resistance. 

P₁R₁ = P₂R₂

⇒ \(P_2 = P_1\frac{R_1}{R_2}\)    ---(1)

Since resistance is directly proportional to length, and 

R₂ = R₁ / 2   ---(2)

Now, putting (2) in (1) we get

P₂ = 2 P₁

So, the power is doubled. 

Why we haven't considered P = I2 R?

• Since the current is not supplied to us. Potential difference is applied. 
• All devices are connected in parallel, and they have same potential difference across them, not current.