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Electric Energy, Power and Household Circuits — Physics STD 10 — Question

ICSE BoardEnglish MediumSTD 10PhysicsElectric Energy, Power and Household Circuits3 Marks
Question
Derive an expression for electric work connecting :
(a) Current, resistance and time,
(b) Current, potential difference and time,
(c) Potential difference, resistance and time
✓

Answer

(a) If W is the amount of work done in carrying charges Q from one point to another point in an electric field, such that V is the potential difference, then
$V=\frac{W}{Q}$...(i)
$\because V = IR $ [Ohm's law]
From (i), $IR =\frac{ W }{ Q }$ or $W = QIR$
Now, $Q = 1 \times t$
$\therefore W = I \times R \times I \times t- I ^2 R t$...(ii)
(b) Now, $Q = I \times t$
From (i), $V =\frac{ W }{I \times t} \quad$ Or $W = V \times I \times t \ldots$ (iii)
(c) $\because I=\frac{V}{R}$
[Ohm's law]
Now, from equation (iii) $W = V \times \frac{ V }{ R } \times t \quad$ or $W =\frac{ V ^2}{ R }, t$...(iv)

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