When two resistors are connected in series to a 13 V battery, the current coming

Question

When two resistors are connected in series to a 13 V battery, the current coming from the battery is 0.5 A. When the same resistors are connected in parallel to the same battery, what is the current coming from the battery if one of the resistors is 6.50 ? _____ A

How much power does the series circuit use? _____ W

How much power does the parallel circuit use? _____ W

How would your answers change if one of the resistors were 13.0 (but the series current were the same as before)?

Parallel circuit current: _____ A
Series circuit power: _______ W
Parallel circuit power: _______ W

Explanation / Answer

let the other resistor be "R"

Rseries = series combination of two resistance = R + 6.50

V = Voltage of battery

iseries = current in series = 0.5 A

using ohm's law

V = iseries Rseries = (0.5) (R + 6.50 )

13 = = (0.5) (R + 6.50 )

R = 19.5 ohm

Rparallel = parallel combination of two resistance = 6.50R/(6.50 + R) = 6.50 x 19.5/(6.50 + 19.5) = 4.875 ohm

V = Voltage of battery = 13

iparalllel = current in parallel

iparalllel = V/Rparallel = 13/4.875 = 2.67 A

Pseries = iseries2 Rseries = (0.5)2 (R + 6.50) = (0.5)2 (19.5 + 6.50) = 6.5 Watt

Pparallel = V2 /Rparallel = (13)2 /4.875 = 34.7 watt

case 2 :

let the other resistor be "R"

Rseries = series combination of two resistance = R + 13

V = Voltage of battery

iseries = current in series = 0.5 A

using ohm's law

V = iseries Rseries = (0.5) (R + 13 )

13 = = (0.5) (R + 13 )

R = 13 ohm

Rparallel = parallel combination of two resistance = 13R/(13 + R) = 13 x 13/(13 + 13) = 6.5 ohm

V = Voltage of battery = 13

iparalllel = current in parallel

iparalllel = V/Rparallel = 13/6.5 = 2 A

Pseries = iseries2 Rseries = (0.5)2 (R + 13) = (0.5)2 (13 + 13) = 6.5 Watt

Pparallel = V2 /Rparallel = (13)2 /6.5 = 26 watt

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.