Compare the power used in the 2resistor in each of the following circuits:
(i) a 6 V battery in series with 1 and 2 a resistors.
(ii) a 4 V battery in parallel with 12 and 2 resistors.
(i) In the First Case:
Potential difference, V = 6 V
And, Net Resistance, R= 1 + 2 = 3 (Resistors are connected in series)
Now, by Ohm’s law:
Thus, the current flowing in the circuit containing 1 and 2 resistors in series is 2 A. In a series circuit, the same current flows throughout the circuit. So, the current flowing through the 2 resistor is also 2A. Now, we know that the current (in 2 resistor) is 2 A and its resistance is 2 .
Now, Power used in 2 resistor is given as:
(ii) In the Second Case:
Here, 4 V battery is attached across the parallel combination of 12 and 2 resistors, so the potential difference across the 2 resistor will also be 4 V. Because in parallel connection
Voltage is same.
Now, Potential difference, V= 4 V
And Resistance, R = 2
So, Power used in 2 resistor, P= =
Thus, the power used in the 2 resistor in the second case is also 8W.
From both the cases we can say that the 2 resistor uses equal power in both the circuits.
Explain the following:
(a) Why is the tungsten used almost exclusively for the 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 are copper and aluminium wires usually employed for electricity transmission?