A piece of wire of resistance $R$ is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is $R'$, then the ratio $\frac{R}{R'}$ is –

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?

Show how you would connect three resistors, each of resistance $6 \Omega$, so that the combination has a resistance of (ii) $4 \Omega$.

Show how you would connect three resistors, each of resistance $6 \Omega$, so that the combination has a resistance of (i) $9 \Omega$,

Compare the power used in the $2 \Omega$ resistor in each of the following circuits: (ii) a 4 V battery in parallel with $12 \Omega$ and $2 \Omega$ resistors.

Compare the power used in the $2 \Omega$ resistor in each of the following circuits: (i) a 6 V battery in series with $1 \Omega$ and $2 \Omega$ resistors, and

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

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

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

Explain the following.
(c) Why is the series arrangement not used for domestic circuits?

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 –

Explain the following.
(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?

An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be –

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

How many $176 \Omega$ resistors (in parallel) are required to carry 5 A on a 220 V line?

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

A copper wire has diameter 0.5 mm and resistivity of $1.6 \times 10^{-8} \Omega$ m. What will be the length of this wire to make its resistance $10 \Omega$? How much does the resistance change if the diameter is doubled?

Explain the following.
(e) Why are copper and aluminium wires usually employed for electricity transmission?

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.

The values of current $I$ flowing in a given resistor for the corresponding values of potential difference $V$ across the resistor are given below –

Plot a graph between $V$ and $I$ and calculate the resistance of that resistor.