Judge the equivalent resistance when the following are connected in parallel –

(a) 1 Ω and 106 Ω,

(b) 1 Ω, 103 Ω, and 106 Ω.

Asked by Vishal kumar | 1 year ago |  218

##### Solution :-

(a) When 1 Ω and 106 are connected in parallel, the equivalent resistance is given by

$$R= \frac{1}{R}=\frac{1}{1}+ \frac{1}{10^4}$$

$$R=\frac{10^6}{1+10^6}\approx\frac{10^6}{10^6} =1Ω$$

Therefore, the equivalent resistance is 1 Ω.

(b) When 1 Ω, 103 Ω, and 106 Ω are connected in parallel, the equivalent resistance is given by

$$\frac{1}{R}=\frac{1}{1}+\frac{1}{10^3}+\frac{1}{10^6}$$

Solving we get

$$R = \frac{10^6+10^3+1}{10^6}=\frac{1000000}{1000001}=0.999 Ω$$

Therefore, the equivalent resistance is 0.999 Ω.

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?