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 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                      = 20.58A                         

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---