Electricity and Magnetism

# Kirchoff's Voltage Law (closed loops)

The above circuit consists of resistors and a voltage source. If voltage source is given as $$V = 16 \text{ V}$$ and the resistances are given as $$R_1 = 2 \Omega$$ and $$R_2 = 4 \Omega,$$ what is the current passing through the resistor $$R_1?$$

Consider the circuit shown in the figure above. The voltages and currents are $v_2 = -2 \text{ V}, v_3 = 8 \text{ V}, v_6= 12 \text{ V}, i_3 = i_4 = i_5 = 4 \text{ A}.$ Determine the values of the voltage across the circuit element $$E.$$

The above circuit consists of resistors and voltage sources. The voltages are given as $$V_1 = 32 \text{ V}$$ and $$V_2 = 16 \text{ V},$$ and the resistances are given as $$R_1 = 2 \Omega, R_2 = 4 \Omega$$ and $$R_3 = 6 \Omega.$$ What is the voltage across the resistor $$R_3?$$

In the above circuit, the voltage source gives $$V = 7 \text{ V}.$$ When the resistance is given by $$R = 2 \Omega,$$ what is the voltage $$V_R$$ across the resistor?

The above circuit consists of resistors and voltage sources. The voltage sources are given as $$V_1 = 90 \text{ V}$$ and $$V_2 = 18 \text{ V},$$ and the resistances are given as $$R_1 = 3 \Omega, R_2 = 6 \Omega$$ and $$R_3 = 9 \Omega.$$ What is the current flow through the resistor $$R_3?$$

Assume that the ground is at the node under the voltage sources.

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