Question

100J heat is generated in a resistance of 4ohm in 1 second.What is the potential difference of the resistor?

Answer 1

Given:

• Heat generated in a resistance = 100 J
• Time = 1 second
• Resistance across the resistor = 4 ohm

To find:

• Potential difference across the resistor?

Solution:

We know that,

• Heating effect of electric current,

★ H = I²Rt

⇏ I² = H/Rt

⇏ I² = 100/4 × 1

⇏ I² = 100/4

⇏ I² = 25

⇏ I = 5 Ampere

Now, Using Ohm's law,

★ V = IR

⇏ V = 5 × 4

⇏ V = 20 V

∴ Potential difference across the resistor is 20 V.

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More to know:

• Ohm's Law: Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference applied across its ends.

Answer 2

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\tt {\pink{Given}}\begin{cases} \sf{\green{Heat\: generated (H) = 100J }}\\ \sf{\blue{Time (t) = 1sec}}\\ \sf{\orange{Resistance (R) = 4Ω}}\end{cases}\end{lgathered} \:\end{lgathered}\end{lgathered}$

⠀

$\huge{\underline{\tt{To\: find }}}$

• Potential difference of the resistor.

⠀

$\huge{\underline{\tt{Solution }}}$

→ To solve this question, we have to find the current by using heating effect of current.

→ Then by using ohm's law we will find the potential difference of the resistor.

★ Heating effect of current

⠀

$\large{\underline{\boxed{\tt{H = I^2Rt}}}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{100 = I^2 × 4 × 1}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{100 = I^2 × 4 }}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{I^2 = \dfrac{100}{4}}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{I^2 = 25}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{I = \sqrt{25}}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{\underline{\boxed{\orange{I = 5A}}}}}$

⠀

★ Using ohm's law

⠀

$\large{\underline{\boxed{\tt{V = IR}}}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{V = 5 × 4}}$

⠀

$\large{\tt:\implies\: \: \: \: \: \:{\underline{\boxed{\orange{V = 20V}}}}}$