a) Five identical resistors, each of resistance R, are connected in series to a

Question

a) Five identical resistors, each of resistance R, are connected in series to a battery, and a current of 2.86 A flows in the circuit. Now, another resistor of resistance R is added to the circuit, in series with the rest of the resistors. Find the new current in the circuit.
_________ A

b) Five identical resistors, each of resistance R, are connected in parallel to a battery, and a current of 2.86 A flows in the circuit. Now, another resistor of resistance R is added to the circuit, in parallel with the rest of the resistors. Fnd the new current in the circuit.
___________ A

c) Five identical resistors, each of resistance R, are connected in series to a battery, and a current of 2.86 A flows in the circuit. Now, another resistor of resistance R is added to the circuit, in parallel with the battery. Find the new total current in the circuit.
______________ A

Explanation / Answer

Let E be the emf of the battery. Resistance of each resistor = R Current I = 2.86 A (a) Total resistance = 5R So Emf E = I 5R = 2.86*5*R = 14.3 R   New current in the circuit I' = E/6R = 14.3R/6R = 2.383 A (b) Total resistance = R/5 So Emf E = I R/5 = 2.86*R/5 = 0.572 R New current in the circuit I' = E/(R/6) = 6E/R = 3.432 A (c) Total resistance = 5R So Emf E = I 5R = 2.86*5*R = 14.3 R New current in the circuit I' = E/[(5R*R)/(5R + R)]                                           = 14.3 R/(5R/6)                                          = 17.16 A (b) Total resistance = R/5 So Emf E = I R/5 = 2.86*R/5 = 0.572 R New current in the circuit I' = E/(R/6) = 6E/R = 3.432 A (c) Total resistance = 5R So Emf E = I 5R = 2.86*5*R = 14.3 R New current in the circuit I' = E/[(5R*R)/(5R + R)]                                           = 14.3 R/(5R/6)                                          = 17.16 A (c) Total resistance = 5R So Emf E = I 5R = 2.86*5*R = 14.3 R Total resistance = 5R So Emf E = I 5R = 2.86*5*R = 14.3 R New current in the circuit I' = E/[(5R*R)/(5R + R)]                                           = 14.3 R/(5R/6)                                          = 17.16 A

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