a) Five identical resistors, each of resistance R, are connected in series to a
ID: 2009476 • Letter: A
Question
a) Five identical resistors, each of resistance R, are connected in series to a battery, and a current of 3.43 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 3.43 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 3.43 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
What I did (It said I was wrong):
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 = 3.43*5*R = 17.15 R
New current in the circuit I' = E/6R = 14.3R/6R = 2.86 A
(b)
Total resistance = R/5
So Emf E = I R/5 = 3.43*R/5 = 0.686 R
New current in the circuit I' = E/(R/6) = 6E/R = 4.12 A
(c)
Total resistance = 5R
So Emf E = I 5R = 3.43*5*R = 17.15 R
New current in the circuit I' = E/[(5R*R)/(5R + R)]
= 17.15 R/(5R/6)
= 20.58 A
Explanation / Answer
a) Given five resistors of resistance R are connected in series combination equivalent resistance of the circuit is R eq = R +R+R+R+R = 5 R voltage across the circuit is V = I R eq = 3.43 * 5R Now, another resistor of resistance R is added to the circuit, in series with the rest of the resistors R' eq = 5R + R = 6R current in the circuit is V = I R'eq I ' = 3.43*5R / 6R = 2.85833 A b) Five identical resistors, each of resistance R, are connected in parallel 1 / R eq = 1/R + 1/R +1/R +1/R+1/R = 5 /R R eq = R / 5 voltage across the circuit is V = I R eq = 3.43 * R /5 Now, another resistor of resistance R is added to the circuit, in parallel with the rest of the resistors R' eq = R / 6 current in the circuit is V = I R'eq I ' = 3.43*R / 5 *6 /R = 4.116A c) Given five resistors of resistance R are connected in series combination equivalent resistance of the circuit is R eq = R +R+R+R+R = 5 R voltage across the circuit is V = I R eq = 3.43 * 5R Now, another resistor of resistance R is added to the circuit, in parallel with the rest of the resistors 1/ R' eq = 1/ 5R + 1/ R R' eq = 5R / 6 current in the circuit is V = I R'eq I ' = 3.43*5R / 5R / 6 = 20.58A equivalent resistance of the circuit is R eq = R +R+R+R+R = 5 R voltage across the circuit is V = I R eq = 3.43 * 5R Now, another resistor of resistance R is added to the circuit, in parallel with the rest of the resistors 1/ R' eq = 1/ 5R + 1/ R R' eq = 5R / 6 current in the circuit is V = I R'eq I ' = 3.43*5R / 5R / 6 = 20.58ARelated Questions
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