Consider the three circuits shown above. All the resistors and all the batteries
ID: 1658783 • Letter: C
Question
Consider the three circuits shown above. All the resistors and all the batteries are identical.
T/F: The total power dissipated in circuit C is twice the total power dissipated in circuit B.
T/F: The current through a resistor is the same in circuits A and B.
T/F: The power dissipated in circuit A is twice the power dissipated in circuit B.
T/F: The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.
T/F: The current through a resistor is the same in circuits A and C.
RRExplanation / Answer
T/F: The total power dissipated in circuit C is twice the total power dissipated in circuit B.
We know P = I^2R Or P = V*I
Calculating Net resistance =>
In circuit C = R/2
In circuit B = 2R
V = Ib*(2R)
Ib = V/(2R)
V = Ic*R/2
Ic = 2V/R
Pb = Ib*V
Pb = V/(2R) = V^2/(2R)
Pc = Ic*V
Pc = (2V/R)*v = 2V^2/R
Hence,
False
T/F: The current through a resistor is the same in circuits A and B.
We know,
V = IR
We have already calculated Ib
Calcuating Ia
V = Ia*R
Ia = V/R
Ib = V/(2R)
Hence,
False
T/F: The power dissipated in circuit A is twice the power dissipated in circuit B.
Pa = V*I = V*(V/R) = V^2/R
We already know
Pb = V^2/(2R)
Hence,
True
T/F: The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.
In circuit B, Voltage across single resistor is V
However in circuit B it is V/2
Hence,
True
T/F: The current through a resistor is the same in circuits A and C.
Ia = V/R
Ic = 2V/R
In circuit C the current in each resistor = Ic/2 = V/r
Hence,
True
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