Circuit question

[sobadsogood]

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A circuit with a battery and 2 resistors in parallel, where R1=R2. If R1 is removed, how will it effect the current through R2?I thought the current will double, but the answer is no change. Could someone let me know why? The explanation it offers is that current through R2 stays same, while current through the battery cut by half.
Thanks

 

[butters221]

Calculate total resistance initially: Rt = (1/(1/R)+1/R) = R/2
Calculate resistance after one of the resistors is removed: Rt = R, Therefore Rt final = 2*Rt initial.
Since the final total resistance is twice the initial total resistance, the total current must have halved: It = Vt/Rt, where Rt doubled.
Since the only resistor left in the circuit is now in series with the battery the total current must also be the current through that resistor.
Now look at what the current through each resistor was initially. According to KCL, currents at the node must = 0. Therefore the total initial current must be equal the sum of the currents going through the resistors. Since the resistors were equal in resistance, each of their currents must have been 1/2 the total current going into the node (total current of the circuit).
Now we calculated 3 steps ago that the current total is 1/2 the initial current total, then we showed that the new current total is also equal to the current through the remaining resistor 2 steps ago, now in the last step we calculated that that the initial current through each resistor was 1/2 the initial total current, therefore the current in the resistor stayed the same, while the current total (same as current through battery) halved.

 

[dudewheresmymd]

A circuit with a battery and 2 resistors in parallel, where R1=R2. If R1 is removed, how will it effect the current through R2?I thought the current will double, but the answer is no change. Could someone let me know why? The explanation it offers is that current through R2 stays same, while current through the battery cut by half.
Thanks

Voltage is same in parallel for all resistors. If R1=R2 let's say 10 V battery and each one 5 ohms. If you remove one resistor in parallel, total resistance goes up (by how much? Rinitial = 2.5 ohms, Rfinal=5 ohms, by a factor of 2). The battery's voltage does not change therefore total circuit voltage does not change. If total voltage does not change and resistance total increased, to maintain same total voltage, total current must decrease (by a factor of 2 since resistance changed by a factor of 2). Now let's look at the ohm's law solely for resistor 2: Voltage through 2=Current through 2*Resistance2 since resistor 2 doesn't change (set by physical property of the resistor remember resistance = resistivity * (L/A), since resistivity is set by the material and length and area of resistor doesn't change, resistance for resistor 2 doesn't change), and voltage through resistor 2 doesn't change (set by parallel battery, voltage supplied to each branch stays the same no matter what, therefore current through resistor 2 will not change. this is a benefit of wiring things in parallel! if you turn off a light "resistor" in parallel, it does not affect the current (flow of charge) through the other devices, even though it does affect total current. ie when you turn off your kitchen lights the current doesn't change in your living room lights in the family room (they don't flicker).

V2=I2*R2, R2 and V2 do not change, therefore current cannot change through resistor 2 even though TOTAL current decreased.

 

[butters221]

V2=I2*R2, R2 and V2 do not change, therefore current cannot change through resistor 2 even though TOTAL current increased.

Everything was correct up until this. Since total resistance increased, total current must have decreased - not increased like you said.

 

[dudewheresmymd]

Everything was correct up until this. Since total resistance increased, total current must have decreased - not increased like you said.

you're right sorry was writing at 2:45 AM, the first sentence in the paragraph is right regarding this, made typo on bottom. fixed! good catch.