Circuit Examples

Which circuit has the smallest resistance?

Ranking Task Rank the total resistance  from smallest to largest

Name this Circuit

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Ex 6)  Series Circuit

a) Find the 'equivalent resistance'

R_T = R₁ + R₂

= 2.0 Ω + 1.0 Ω

= 3.0 ohms

b) Find the current (I_T) going through this circuit

V_T = I_TR_T

12. Volt = I_T(3.0 ohms)

I_T = 4.0 amps

c) Find potential drop across R₁ & R₂

V = IR

V₁=4.0 amps(2.0 ohms)

= 8.0 Volts

V₂ =4.0 amps(1.0 ohms)

= 4.0 Volts

Ex 7)

a) Find combined resistance (R_T)

V_T = I_T R_T

60. volts = (10 amps)R_T

= 6.0 ohms

b) Find the current in R₁

V₁ = I₁R₁

60. Volts = I₁20. ohms

I₁ = 3.0 amps

c) Find I₃

V₃ = V_T = 60. volts

Use Ohm's Law

V₃ = I₃R₃

60. volts = I₃30. ohms

I₃  = 2.0 amps

d) Find R₂

e) Find value of the second resistor

Ex 8)

If the voltage drop across the 3 ohms resistor is 4.0 volts then the voltage drop across the 6.0 ohm resistor is

3.0 ohms : 4.0 volts

6.0 ohms : x

x = 8.0 volts

a) Find the total voltage in this series circuit

V_T = V₁ + V₂

V_T = 8.0 V + 4.0 V

= 12 V

b) Find combined resistance in this circuit

R_T = 6.0 ohms + 3.0 ohms

R_T = 9.0 ohms

c) Total current in this circuit?

V_T = I_TR_T

 12 V = I_T(9.0 ohms)

I_T  = 1.3 Amps

Ex 9)

a) Compare the current through each resistor

Same (Series Circuit)

I_T = I₁ = I₂ = ... 

b) Compare the voltage drops in this circuit?

20. ohm resistor has twice the potential difference (voltage)

c) Current in this circuit?

V_T = I_TR_T 

60. V =  I_T(30. ohms)

I_T  = 2.0 Amps

c) Potential difference in 20. ohm resistor?

V = IR

= 2.0 amps(20. ohms)

= 40. V

Ex 10) Find R₂

August Sampler

V = IR

First Find R_T

8 V = 1 Amp(R_T)

R_T  = 8 ohms

Find R₂

R_T = R₁ + R₂

_Since

R_T  = 8 ohms

R = 6 ohms

Parallel Circuit Game 26
Test your knowledge of Parallel Circuits

AP Circuits

EMF - max. voltage of source

- internal resistance causes actual V to be lower

Complex Circuits

Ex) Find the potential difference between  X and Y

Convert parallel R to a single R

1/R_T = 1/3 + 1/6

1/R_T = 3/6

R_T = 2 ohms

Series Circuit 4 ohms,
2 ohms, 6 V source

Need V across 2 ohm R

V  = IR

V_T  = I_TR_T

6 V  = I_T6 ohms

 I_T = 1 amp

V = 2 V

Ex 2)

Find equivalent R between X and Y

1/R_T = 1/3 + 1/6

R_T = 2 ohms

R_T = 3 ohms

Ex 3)

Find total current

(A)  0.8 mA   (B)  1.0 mA 

 (C)  2.0 mA  (D) 3.0 mA (E) 6.0 mA

Reduce parallel R to single R

1/R_T=1/2000+1/6000

1/R_T=3/6000+1/6000

R_T = 1500 ohms

V = IR

12 V = I[4000 ohms]

(A)  0.8 mA   (B)  1.0 mA 

 (C)  2.0 mA  (D) 3.0 mA (E) 6.0 mA

Attaching Meters

Enrichment