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

Question

1)
a) Five identical resistors, each of resistance R, are connected in series to a battery, and a current of 8.27 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 8.27 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 8.27 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 = 8.27 A (a) Total resistance = 5R So Emf E = I 5R = 8.27*5*R = 41.35 R   New current in the circuit I' = E/6R = 41.35 R/6R = 6.891 A
(b) Total resistance = R/5 So Emf E = I R/5 = 8.27*R/5 = 1.654 R New current in the circuit I' = E/(R/6) = 6E/R = 9.924 A
(c)
Total resistance = 5R
So Emf E = I 5R = 8.27*5*R = 41.35 R
New current in the circuit I' = E/[(5R*R)/(5R + R)]
                                          = 41.35 R/(5R/6)
                                         = 49.62 A

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