Consider the three circuits shown above. All the resistors and all the batteries

Question

Consider the three circuits shown above. All the resistors and all the batteries are identical.

Consider the three circuits shown above. All the resistors and all the batteries are identical. The current through a resistor is the same in circuits A and B. The current through a resistor is the same in circuits A and C. The power dissipated in circuit A is twice the power dissipated in circuit B. The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B. The total power dissipated in circuit C is twice the total power dissipated in circuit B.

Explanation / Answer

a)

False

V = I * R

and I = V / R

since the resistance is greater in B it has less current

b)
true

the current in C is twice that in A since

I = V / R

and the resistance in C is R/2

But, it is split among two equal resistors. So, each carries half that amount of current. Thus, the current through a resistor in C is the same as the current through the resistor in A

c)

true

P = V^2/R

the resistance in B is twice that in A so A dissipates twice the power

d)

true

each resistor in C has the entire voltage drop across it. However, circuit B has two equal resistors in series, so the voltage must drop across each of them. Since they are equal resistance, the voltage drops half of its full amount across each one

e)

false

the equivalent resistance of C is

2 / (1/R+1/R) = R/2

then

P = V^2 * (1/R/2)

P = 2 * V^2 / R

which is four times that of B

P = V^2 / 2*R

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