Combining Resistors in Series & Parallel Video Lessons

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Problem: Consider the five networks shown at right.a. Rank the networks according to equivalent resistance, from largest to smallest. (Hint: Imagine placing each network in series with an indicator bulb and a battery.)b. How does adding a single bulb to a circuit in series with another bulb or network affect the resistance of the circuit?c. How does adding a single bulb to a circuit in parallel with another bulb or network affect the resistance of the circuit?d. The networks A-E are connected, in turn, to identical batteries as shown.Use the model we have developed to:• rank the circuits according to equivalent resistance, from largest to smallest. Explain.• rank the circuits according to the current through the battery, from largest to smallest. Explain.

FREE Expert Solution

Equivalent resistance for resistors in parallel:

1Req=1R1+1R2+...+1Rn

or for 2 resistors:

Req=R1R2R1+R2

Equivalent resistance for resistors in series:

Req=R1+R2+...+Rn

a.

We'll assume that all the bulbs have equal resistance, R.

A is a single resistor. Resistance = R

B is two resistors in series. 

Req = R1 + R2 = R + R = 2R

C is two resistors in parallel. 

Req = R1R2/(R1 + R2) = R•R/(R + R) = R2/2R = R/2

D is a short circuit with zero resistance. 

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Problem Details

Consider the five networks shown at right.

a. Rank the networks according to equivalent resistance, from largest to smallest. (Hint: Imagine placing each network in series with an indicator bulb and a battery.)

b. How does adding a single bulb to a circuit in series with another bulb or network affect the resistance of the circuit?

c. How does adding a single bulb to a circuit in parallel with another bulb or network affect the resistance of the circuit?

d. The networks A-E are connected, in turn, to identical batteries as shown.

Use the model we have developed to:

• rank the circuits according to equivalent resistance, from largest to smallest. Explain.

• rank the circuits according to the current through the battery, from largest to smallest. Explain.

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