Question

Heat energy is being produced in a
resistance in a circuit at the rate of
100 W. The current of 3 A is flowing
in the circuit. What must be the
value of the resistance?​

Answer 1

${\large{\underline{\underline{\bf{Given\::}}}}}$

Rate of power, (P) = 100 Watt

Current, (i) = 3 Ampere

${\large{\underline{\underline{\bf{Explanation\::}}}}}$

As we know that formula of the electrical power;

$\boxed{\sf{P = i^{2}R}}$

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

$\longrightarrow\sf{100 = (3)^{2}\times R}$

$\longrightarrow\sf{100 = 3 \times 3\times R}$

$\longrightarrow\sf{100 = 9\times R}$

$\longrightarrow\sf{R = \cancel{\dfrac{100}{9} }}$

$\longrightarrow\sf{R = 11.11\:\Omega}$

Thus,

The value of the resistance will be 11.11 Ω

${\star\: {\large{\boxed{\mathfrak{\purple{Note\::}}}}}}$

1 horse power = 746 Watt

Number of joules in kilowatt-hour = 3.6 × 10^6

The unit of electric power = Watt (W)

The commercial unit of electrical energy = kilowatt-hour, (kwh)

1 kwh = 3600000 joules

Answer 2

Step-by-step explanation:

${\large{\underline{\underline{\bf{Given\::}}}}}$

Rate of power, (P) = 100 Watt

Current, (i) = 3 Ampere

${\large{\underline{\underline{\bf{Explanation\::}}}}}$

As we know that formula of the electrical power;

$\boxed{\sf{P = i^{2}R}}$

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

$\longrightarrow\sf{100 = (3)^{2}\times R}$

$\longrightarrow\sf{100 = 3 \times 3\times R}$

$\longrightarrow\sf{100 = 9\times R}$

$\longrightarrow\sf{R = \cancel{\dfrac{100}{9} }}$

$\longrightarrow\sf{R = 11.11\:\Omega}$

Thus,

The value of the resistance will be 11.11 Ω

${\star\: {\large{\boxed{\mathfrak{\pink{Note\::}}}}}}$

1 horse power = 746 Watt

Number of joules in kilowatt-hour = 3.6 × 10^6

The unit of electric power = Watt (W)

The commercial unit of electrical energy = kilowatt-hour, (kwh)

1 kwh = 3600000 joules