(i) T be the current flowing through a resistor of resistance 'R' and 'V' be the potential difference across the resistor. The charge flowing through the circuit for a time interval 't' is 'Q':
(ii) The work done in moving the charge Q across the ends of the resistor with a potential difference of V is VQ. This energy spent by the source gets dissipated in the resistor as heat. Thus, the heat produced in the resistor is:
H = W = VQ
(iii) You know that the relation between the charge and current is Q = I t. Using this, you get
H = V I t ------------------------ (A)
From Ohm's Law, V = I R. Hence, you have
H = I² R t ------------------------ (B)
This is known as Joule's law of heating.

A connection of a set of series resistors connected in a parallel circuit, is a parallel-series circuit. Let R₁ and R₂ be connected in series to give an effective resistance of R_s1. Similarly, let R₃ and R₄ be connected in series to give an effective resistance of R_s2. Then, both of these serial segments are connected in parallel (Figure).

Using the equation R_s = R₁ + R₂
R_s1 =R₁ + R₂'
R_S2 = R₃ + R₄
Finally, using equation \(\left( \frac { 1 }{ { R }_{ p } } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } \right) \), the net effective resistance is given by \(\frac { 1 }{ { R }_{ total } } =\frac { 1 }{ { R }_{ S1 } } +\frac { 1 }{ { R }_{ S2 } } \)

The connection of a set of parallel resistors that are connected in series, is a series - parallel circuit
Let R₁ and R₂ be connected in parallel to give an effective resistance of R_p1. Similarly, let R₃ and R₄ be connected in parallel to give an effective resistance of R_p2. Then, both of these parallel segments are connected in series (Figure).

For parallel connection, the effective resistance is \(\frac { 1 }{ { R }_{ p } } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } \)
Using equation
\(\frac { 1 }{ { R }_{ p1 } } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } \)
\(\frac { 1 }{ { R }_{ p2 } } =\frac { 1 }{ { R }_{ 3 } } +\frac { 1 }{ { R }_{ 4 } } \)
R_p1 & R_p2 are connected in series Finally, using equation R_s = R₁ + R₂ the net effective resistance is given by
\({ R }_{ total }={ R }_{ p1 }+{ R }_{ p2 }\)

(i) A series circuit connects the components one after the other to form a 'single loop'. A series circuit has only one loop through which current can pass.
(ii) A parallel circuit has two or more loops through which current can pass. If the circuit is disconnected in one of the loops, the current can still pass through the other loop(s).

(i) Resistor is used to fix the magnitude of the current through the circuit
(ii) Rheostat is used to fix the magnitude of the current through the circuit
(iii) Ammeter is used to measure the current.
(iv) Voltmeter is used to measure the potential difference.

Resistance of an ammeter should be low because almost all the current in the circuit is allowed to pass through ammeter.

(i) V = IR
(ii) H = I²Rt
(iii) R_s = R₁ + R₂
(iv) P = VI
(v) \(\rho=R\frac{A}{L}\)

40W. for the same applied voltage, power \(\alpha \frac{1}{resistance}\) If the power is less, higher will be its resistance.

(i) When temp is increased, resistance is increased
(ii) When length is doubled, resistance is increased
(iii) When area of cross section is increased, resistance is increased.

Copper wire is used as connecting wires because copper has very low resistivity.