Equivalent resistance of parallel circuits

The voltage in the two circuits below is the same, but the two-bulb circuit draws more total current. Why? To answer the question, consider that current flowing out of the battery obeys Ohm’s law. The current is the battery voltage divided by the total resistance of the circuit. What resistance does the battery “see?” Read the text aloud
Current through single bulb and two bulb parallel circuits
According to Ohm’s law, the current in each branch of the circuit is the battery voltage V divided by the resistance of that branch (R1 or R2). Next, note that the current flowing out of the battery is the sum of the currents in the two branches (from Kirchhoff’s current law). Read the text aloud
Compare the equations for current to determine the parallel resistance equation
If you compare this with Ohm’s law, the inverse of the total resistance as seen by the battery is equal to the sum of the inverses of the individual branch resistances. This leads directly to equation (17.4), which gives the total resistance R for a parallel circuit containing three individual resistances: Read the text aloud
(17.4) 1 R = 1 R 1 + 1 R 2 + 1 R 3 +
R  = equivalent resistance (Ω)
R1  = resistance 1 (Ω)
R2  = resistance 2 (Ω)
R3  = resistance 3 (Ω)
Equivalent resistance
parallel resistors
Adding more branches to a parallel circuit always increases the total current in the circuit. From the perspective of the battery, the total resistance of the circuit must decrease, because more total current flows while the voltage stays the same (equation 17.4). Read the text aloud
What is the equivalent resistance of two 10 Ω resistors connected in parallel?
Asked: equivalent resistance Req
Given: individual resistances R1 = 10 Ω and R2 = 10 Ω
Relationships:
1 R = 1 R 1 + 1 R 2 + 1 R 3 +
Solution: Add the resistances by finding a common denominator:
1 R eq = 1 R 1 + 1 R 2 = 1 10 Ω + 1 10 Ω = 1+1 10 Ω = 1 5 Ω
If (1/Req) = 1/(5 Ω), then Req = 5 Ω.
Answer: Req = 5 Ω.
Read the text aloud
If you connect three identical resistors in series and in parallel, in which case will they have a smaller equivalent resistance? Show

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