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Derive an expression for the heat produced in a conductor of resistance R when a current flow throughif for time t. Two identical resistors of resistance R are connected in series with a battery of potential difference V for time t. the resistors are then connected in parallel with the same battery for the same time t. Compare the heat produced in the two cases Please tell now |
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Answer» Derivaƭon: For work done, , on moving W a NET charge, , the potential difference is defined as, Q V = QW ⇒ W = VQ Let be the time it takes to move the net charge t . Multiplying and dividing the R.H.S. by , weget, Q W = V ×× t t = VIt Q where is the current, , by definition. [ mark] t 1 I Since this work is converted into HEAT energy, we can write, W = H = VIt =(IR)× It 2 H = IRt where is the resistance in the circuit and R Ohm's law () is applied in the second step. [ mark] V = IR 1 Second part: We obtained, . W = H = VIt I = RV Writing from Ohm's law, we get,H = V ×× t V 2 = t R H ∝ R1 [ mark] 1 If two EQUAL resistances, each, are connected R in series, the equivalent resistance, R = S R + R =2R. When connected in parallel, the equivalent resistance, , is found as, 1 RP RP 1 =+ R R RP = 2R [ mark] 1 1 Let the heat produced in the series combination be , and the parallel HS combination be . We have,HS 1/RS HP = 1/RP RP = RS R =× 2R 2 1 P HS = H 4 HP =4HS 1 Therefore, the heat produced in the parallel combination is four times that of the series combination. [ mark] Explanation: |
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