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. 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. Tries 0/30

Explanation / Answer

first circuit:

total resistance=R

voltage=V

current=V/R

circuit B:

R and R are in series.

net resistance=R+R=2*R

current=V/(2*R)

circuit C:

R and R in parallel.

net resistance=R*R/(R+R)=R/2

current in the circuit=V/(R/2)=2*V/R

then:

first statement is false as current through a resistor is different for circuit A and circuit B.

second statement:

power dissipated in circuit C=voltage^2/total resistance

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

power dissipated in circuit B=V^2/(2*R)

so total power dissipated in circuit C is 4 times total power dissipated in circuit B.

hence the given statement is false.

third statement:

power dissipated in circuit A=V^2/R

hence it is double of power dissipated in circuit B.

hence the statement is correct.

fourth statement:

voltage across R in both circuit A and circuit C is same as V.

hence current through a resistor is same.

hence the statement is true.

fifth statement:

voltage across a single resistor in circuit C=V

voltage across a single resistor in circuit B=(V/(R+R))*R=V/2

hence the statement is correct.

so answers are:

false

false

true

true

true

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