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# Electrical circuits with capacitors and resistances

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Electrical circuits with capacitors and resistances. See attached file for full problem description.

##### Solution Summary

Twelve questions with resistances and capacitors in series and parallel. The current, charges, voltage etc are calculated.

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1.
The junction rule describest he conservation of which quantity? Note that this rule applies only to circuits that are in steady state.
. current

voltage

resistance

The answer is current, as this rule says that the algebraic sum of the current is zero or total inward current is equal to total outward current.

Part B
Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance ).
Answer in terms of given quantities, together with the meter readings and and the current .

- I1 + I2 + I3

I2 and I3 are incoming currents and I1 is outgoing current.

Part C
Apply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow. Remember that the current meter is ideal.
Express the voltage drops in terms of , , , the given resistances, and any other given quantities.

I2R2 - I3R3

As the current in R2 is in the direction of the loop and that in R3 is opposite.

Part D
Now apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.
Express the voltage drops in terms of , , , the given resistances, and any other given quantities.

- Vb + I1R1 + I3R3

as the voltage gain at the cell and drop at the resistors.

2.

What is the effective resistance of the two-resistor system?
Express the effective resistance in terms of and .
=
R1 + R2

The two resistors are in series.

Three Resistors in Series

Now consider three resistors set up in series, as shown.

The resistances are , , and , and the applied constant voltage is again .
Part B
Find the effective resistance, , of the three-resistor system.
Express the effective resistance in terms of , , and .
=
R1 + R2 + R3

3.
Which two of the following statements are true?
1. The voltage source provides a constant voltage, a part of which, , drops off across resistor 1, and the remainder, , across resistor 2. Hence .
2. The voltage drops across resistor 1 and across resistor 2 are the same, and they are independent of the ...

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