Question

800J of heat is produced each second in a 2 ohm resistance find the potential difference across the resistor​

Answer 1

Answer:

Given :-

• 800 J of heat is produced each sound in a 2 ohm resistance.

To Find :-

• What is the potential difference across the resistor.

Formula Used :-

$\clubsuit$ Heat Produced Formula :

$\mapsto \sf\boxed{\bold{\pink{H =\: I^2Rt}}}$

where,

• H = Heat Produced
• I = Electric Current
• R = Resistance
• t = Time Taken

$\clubsuit$ Potential Difference Formula :

$\mapsto \sf\boxed{\bold{\pink{V =\: IR}}}$

where,

• V = Potential Difference
• I = Electric Current
• R = Resistance

Solution :-

First, we have to find the current :

Given :

• Heat Produced = 800 J
• Resistance = 2 Ω
• Time Taken = 1 seconds

According to the question by using the formula we get,

$\implies \sf 800 =\: I^2 \times (2)(1)$

$\implies \sf 800 =\: I^2 \times 2 \times 1$

$\implies \sf 800 =\: I^2 \times 2$

$\implies \sf \dfrac{\cancel{800}}{\cancel{2}} =\: I^2$

$\implies \sf 400 =\: I^2$

$\implies \sf \sqrt{400} =\: I$

$\implies \sf \sqrt{\underline{20 \times 20}} =\: I$

$\implies \sf 20 =\: I$

$\implies \sf\bold{\purple{I =\: 20\: A}}$

Now, we have to find the potential difference across the resistor :

Given :

• Electric Current = 20 A
• Resistance = 2 Ω

According to the question by using the formula we get,

$\longrightarrow \sf V =\: (20)(2)$

$\longrightarrow \sf V =\: 20 \times 2$

$\longrightarrow \sf\bold{\red{V =\: 40\: V}}$

${\small{\bold{\underline{\therefore\: The\: potential\: difference\: across\: the\: resistor\: is\: 20\: V\: .}}}}$