10.2 Combing Resistors | 10.3 Analysing circuits

How does adding resistors affect a series circuit?

The length of the path taken by the charges gets longer so resistance increases. Rtotal = R1 + R2…

How can the relationship be derived from Kirchoff's laws?

Second law: The total p.d is equal to the sum of the p.ds across each resistor:

Vtotal = V1 + V2 + …

Because V = IR, this can be rewritten as IRtotal = IR1 + IR2 + ….

First law: Current through each resistor must be the same so I is a constant, giving : Rtotal = R1 + R2 + ….

How does adding resistors affect parallel circuits?

The total resistance drops because another path is provided for the current. This effectively increases the cross sectional area and so lowers the resistance.

How can the relationship be derived from Kirchoff's laws?

First law: total current is equal to sum of the current in each resistor, giving Itotal = I1 + I2 +…

Second law: the p.d across each resistor is constant and must be equal to V. Dividing the first equation by V gives: I/V = I1/V + I2/V +…

V = IR so I/V = 1/R so 1/Rtotal = 1/R1 + 1/R2 +…

What are resistor circuits?

Different combinations of resistors in series and parallel.

What equations should be used when tackling circuit questions?

I = change in Q/change in t

V = W/Q

P = VI

V = IR

How is internal resistance related to lost volts?

If you apply V = IR to internal resistance you can see that

lost volts = I × r

Where r is the internal resistance. If r is fixed then the current in the power source is directly proportional to the lost volts.

How is e.m.f related to terminal p.d?

The e.m.f is always more than the terminal p.d unless there is no current. When the current is very small e.m.f ≈ V.

Derive an equation for e.m.f for a power source:

Combining:

E.m.f = V + lost volts

E.m.f = V + IR

Terminal p.d is also equal to IR where R is the resistance of the circuit so

E.m.f = IR + Ir

As the current through the circuit and through the power supply must be the same, I is a common factor

E.m.f = I(R + r)

This relationship is essentially a version of V = IR that takes into account the internal resistance of the power source.