Question

if a charge of 3.75 X 10^4 C flows through an electric heater and the amount of electric heater and the amount of electrical energy converted into heat is 9MJ, calculate the potential difference across the end of the heater.

Answer 1

Hello Dear.

Here is the answer---

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Given Conditions ⇒ 

Charge(Q) = 3.75 × 10⁴ C.
Heat Energy(H) = 9 MJ
                          = 9 × 10⁶ J.

Using the Formula,

 H = I² R t
Where,
I = Current
R = Resistance
t = time

Also, I = Q/t
     
        H = I × I × R × t
Thus, H = I × Q/t × R × t
   ⇒  H = I × R × Q

∵ I × R = V  [By Ohm's Law]

∴ H = V × Q
∴ V = H/Q
  V = (9 × 10⁶) ÷ (3.75 × 10⁴)
  V =  9/3.75 × 100
  V = 2.4 × 100
 V = 240 V.


Thus, the Potential Difference across the Conductor is 240 V.


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Hope it helps.

Have a Good Day.

Answer 2

Electrical potential energy is given by
E = VQ , where V is potential difference and Q is charge.

Given,
Electrical energy converted into heat = 9MJ = 9 × 10⁶ J
e.g., E = 9 × 10⁶J
charge flows through electric heater = 3.75 × 10⁴ C
e.g., Q = 3.75 × 10⁴ C

∴ 9 × 10⁶ = V × 3.75 × 10⁴
⇒ V = 900/3.75
⇒V = 240 V

Hence, potential difference across the end of the heater is 240V