Question 380: Current Electricity

Question

When  the switch  S, in the circuit shown, is closed, then the value of current i will be :

Accepted Answer

We start by applying Kirchhoff's current law at point C in the circuit:
$$i_1+i_2=i$$
where $i_1$ and $i_2$ are the currents flowing through resistors R
1
and R
2
respectively, and i is the current flowing through the battery and resistor R
3
.
Next, we use Ohm's law to express $i_1$ and $i_2$ in terms of the voltages at points A, B, and C:
$$i_1=\frac{V_A-V_C}{R_1}=\frac{20-V_C}{2}$$
$$i_2=\frac{V_B-V_C}{R_2}=\frac{10-V_C}{4}$$
where $R_1$ and $R_2$ are the resistances of resistors R1 and R2 respectively.
Substituting these expressions into the first equation, we get:
$$\frac{20-V_C}{2}+\frac{10-V_C}{4}=i$$
We then use Ohm's law again to express i in terms of the voltages at points C and earth :
$$i=\frac{V_C-V}{R_3}=\frac{V_C-0}{2}=\frac{V_C}{2}$$
Substituting this expression into the previous equation, we get:
$$\frac{20-V_C}{2}+\frac{10-V_C}{4}=\frac{V_C}{2}$$
Simplifying this equation, we get:
$$40-2V_C+10-V_C=2V_C$$
$$50=5V_C$$
$$V_C=10	ext{ V}$$
Finally, we use Ohm's law to find the value of the current i:
$$i=\frac{V_C}{2}=\frac{10}{2}=5	ext{ A}$$
Therefore, the current flowing through the circuit is 5 A.

Answer

3A

Answer

5A

Answer

4A

Answer

2A

Current Electricity

When the switch S, in the circuit shown, is closed, then the value of current i will be :

Choose the correct answer: