A filament bulb (\(500\) W, \(100\) V) is to be used in a \(230\) V main supply. When a resistance\(R\) is connected in series, the bulb works perfectly and consumes \(500\) W. The value of \(R\) is:

Two cities are \(150~\text{km}\) apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is \(8\) volts and the average resistance per km is \(0.5~\text{ohm}\). The power loss in the wire is:
1. \(19.2~\text{W}\)
2. \(19.2~\text{kW}\)
3. \(19.2~\text{J}\)
4. \(12.2~\text{kW}\)

If the voltage across a bulb rated \((220~\text{V}\text-100~\text{W})\) drops by \(2.5\%\) of its rated value, the percentage of the rated value by which the power would decrease is:
1. \(20\%\)
2. \(2.5\%\)
3. \(5\%\)
4. \(10\%\)

The power dissipated in the circuit shown in the figure is \(30~\text{Watts}\). The value of \(R\) is:
    
1. \(15~\Omega\)
2. \(10~\Omega\)
3. \(30~\Omega\)
4. \(20~\Omega\)

If power dissipated in the 9 $\mathrm{\Omega }$ resistor in the circuit shown is 36 W, the potential difference across the 2 $\mathrm{\Omega }$ resistor will be:

A thermocouple of negligible resistance produces an e.m.f. of 40 µV/ºC in the linear range of temperature. A galvanometer of resistance 10 ohm whose sensitivity is 1 µA/division, is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be:
1. 0.25ºC
2. 0.5 ºC
3. 1ºC
4. 0.1ºC

A current of \(3~\text{A}\) flows through the \(2~\Omega\) resistor shown in the circuit. The power dissipated in the \(5~\Omega\) resistor is: