Question

200J of heat produce in 4 second a resestor of resistance 8 volt find the potential difference across the resestor and it's power

Answer 1

CORRECT QUESTION:

200J of heat produce in 4 second a resestor of resistance 8 ohm. Find the potential difference across the resistor and it's power.

SOLUTION:

• Heat produced, H = 200 J

• Time, t = 4 seconds

• Resistance , R = 8 ohm

• Let V be the potential difference.

• Let P be the power.

POWER:

We know that,

Power is defined as the rate of doing work.

Here work is also referred to as energy.

Power = Work / Time

Power = Work / TimePower = Heat produced / Time

P = H/t

$P = \frac{200}{4} \\ \\ P= 50 \: watt$

The power across the resistor is 50 watt.

POTENTIAL DIFFERENCE:

We know that,

Power, P = V²/R

$50 = \dfrac{ {V}^{2} }{8} \\ \\ {V}^{2} = 50 \times 8 \\ \\ {V}^{2} = 400 \\ \\ V = \sqrt{400 } \\ \\ V = 20 \: volt$

Potential difference across the resistor is 20 volt.

Answer 2

Appropriate Question :-

→ 200J of heat produce in 4 seconds a resistor of resistance 8 ohms find the potential difference across the resistor and it's power

Given :-

→ Heat (H) = 200 J

→ Time (t) = 4s

→ Resistance (R) = 8 ohms

To Find :-

→ Potential Difference (V) across the resistor

→ Power (P) across the resistor

Solution :-

→ Here , the work done is represented by heat energy .

${\huge{\red{\boxed{\underline{Power\;=\;\dfrac{Heat\;produced}{Time} }}}}}$

$\sf P \; = \; \dfrac{H}{t}\\ \\\\\longrightarrow \dfrac{200}{4} \\\\\longrightarrow 50 \; watts$

∴ Power across the resistor is 50 watts .

→ As we know that ,

$\Large{\boxed{\underline{\underline\red{Power \;=\; \dfrac{V^{2} }{R} }}}$

$\sf \longrightarrow 50 = \dfrac{V^{2} }{8} \\\\\longrightarrow V^{2} = 50 \times 8 \\\\\longrightarrow V^{2} = 400 \\\\\longrightarrow V = \sqrt{400} \\\\\longrightarrow V = 20 \; volts$

∴ Potential difference across the resistor is 20 volts .

All Done ! :D