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 arc identical. Select true or false for each statement. The current through a resistor is the same in circuits A and B. The total power dissipated in circuit C is twice the total power dissipated in circuit B. The power dissipated in circuit A is twice the power dissipated in circuit B. The current through a resistor is the same in circuits A and C. The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.

Explanation / Answer

a)

false

ia = current in A = total Voltage /total resistance = V/R

ib = current in B = total Voltage /total resistance = V/2R

b)

Pb = power dissipated in B = V ib = V (V/2R) = V2/(2R) = (0.5) V2/(R)

Pc = power dissipated in C = V ic = V (V/(R/2)) = 2V2/(R)

hence false

c)

Pa = power dissipated in A = V ia = V (V/R) = V2/(R)

Pb = power dissipated in B = V ib = V (V/2R) = V2/(2R) = (0.5) V2/(R)

Pa = 2 Pb

hence true

d)

True

e)

True

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