Electricity Worksheet-15

Electricity Worksheet-15

1. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit.  Find the value of the resistance of the resistor.

2. A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω and 12 Ω. How much current would flow through the 12 Ω resistor ?

3. How many 176 Ω resistors (in parallel) are required to carry 5 A in 220 V line ?

4. Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of 9 Ω and 2 Ω.

5. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A ?

6. A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series or in parallel. What are the currents in the three cases ?

7. Compare the power used in the 2 Ω resistor in each of the following circuits :

(a) a 6 V battery in series with 1 Ω and 2 Ω resistors,

(b) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

8. 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 ?

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

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

Answer:

1. V = 12 V, I = 2.5 mA = 2.5 × 10^–3 A

Resistance of the resistor,  

2. Since all the resistors are in series, equivalent resistance,

Current through the circuit,  

In series, same current flows through all the resistors. Thus, current flowing through 12 Ω resistor   

                   = 0.67 A

3. I = 5 A, V = 220 V.

Resistance required in the circuit,

Resistance of each resistor r = 176 Ω

If n resistors, each of resistance r, are connected in parallel to get the required resistance R, then or or

To get a resistance of 9 Ω from three resistors, each of resistance 6 Ω, we connect two resistors in parallel and this parallel combination in series with the third resistor.

To get a resistance of 2 Ω from three resistors, each of resistance 6 Ω, we connect all the three resistors in parallel as equivalent resistance in parallel combination, i.e.,

R_p is given by

Resistance of each bulb, 

Total resistance in the circuit,

Let n be the number of bulbs each of resistance r to be connected in parallel to get a resistance R.

          110

6. Potential difference  V = 220 V

resistance of each coil r = 24 Ω

(a) When each of the coils A or B is connected separately, current through each coil,

(b) When coils A and B are connected in series, equivalent resistance in the circuit,

Current through the series combination, i.e., 

(c) When the coils A and B are connected in parallel, equivalent resistance in the circuit,

Current through the parallel combination, i.e., 

          18.3 A

7. (i) Since 6 V battery is in series with 1 Ω and 2 Ω resistors, current in the circuit,

Power used in 2 Ω resistor,

(ii) Since 4 V battery is in parallel with 12 Ω and 2 Ω resistors, potential difference across 2 Ω resistor, V = 4 V.

Power used in 2 Ω resistor,

Clearly, 

8. Resistance of first lamp, 

resistance of the second lamp,

Now, the two lamps are connected in parallel, the equivalent resistance is given by

or     

Current drawn from the line, i.e.,   

9. Energy used by TV set in 1 h = 250W × 1h = 250 Wh

Energy used by toaster in 10 min. (i.e., 1/6 h) = 1200 W × (1/6)h = 200 Wh

Hence a 250 W TV set uses more power in 1 h than a 1200 W toaster in 10 minutes.

10. Here, I = 15 A, R = 8 Ω, t = 2 h

Rate at which heat is developed, i.e., electric power,

P = I² R = (15)² × 8 = 1800 W = 1800 J/s