Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be _____.

(a) 1:2

(b) 2:1

(c) 1:4

(d) 4:1

Asked by Vishal kumar | 1 year ago |  150

##### Solution :-

Let Rs and Rp be the equivalent resistance of the wires when connected in series and parallel, respectively. For the same potential difference V, the ratio of the heat produced in the circuit is given by

$$\frac{H_s}{H_p}=\frac{\frac{V^2}{R^s}t}{\frac{V^2}{R_p}t}=\frac{R_p}{R_s}$$

The equivalent resistance of resistors connected in series R, is R+R = 2R

The equivalent resistance of resistors connected in parallel Rp is $$\frac{1}{\frac{1+1}{R+R}}=\frac{R}{2}$$

Hence, the ratio of the heat produced in series and parallel combination would be

$$\frac{H_p}{H_s}=\frac{\frac{R}{2}}{2R}=\frac{1}{4}$$

Hence, the ratio of the heat produced is 14

Answered by Shivani Kumari | 1 year ago

### Related Questions

#### Explain the following. a. Why is the tungsten used almost exclusively for filament of electric lamps?

Explain the following.

a. Why is the tungsten used almost exclusively for filament of electric lamps?

b. Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?

c. Why is the series arrangement not used for domestic circuits?

d. How does the resistance of a wire vary with its area of cross-section?

e. Why copper and aluminum wires are usually employed for electricity transmission?

#### An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater

An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.

#### Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?

Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?

#### Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected

Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is 220 V?