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 = I^{2} R = V^{2} / 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.

P_{1}R_{1} = P_{2}R_{2}

⇒ \(P_2 = P_1\frac{R_1}{R_2}\) ---(1)

Since resistance is directly proportional to length, and

R_{2} = R_{1} / 2 ---(2)

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

P_{2} = 2 P_{1}

**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.